statcpp Namespace Reference

Namespaces
namespace	detail
	Internal helper functions.

Classes
struct	aggregation_result
	Aggregation result per group. More...
struct	ancova_result
	Structure storing ANCOVA (Analysis of Covariance) results. More...
struct	anova_row
	Structure representing a row in the ANOVA table. More...
struct	bootstrap_result
	Structure to store bootstrap estimation results. More...
struct	complete_case_result
	Complete case analysis result. More...
struct	confidence_interval
	Structure to store confidence interval results. More...
struct	contingency_table_result
	Contingency table (cross-tabulation) result. More...
struct	cv_result
	Structure to store cross-validation results. More...
struct	dendrogram_node
	Dendrogram node. More...
struct	five_number_summary_result
	Five-number summary result. More...
struct	frequency_entry
	Frequency table entry. More...
struct	frequency_table_result
	Frequency table result. More...
struct	glm_residuals
	GLM residuals structure. More...
struct	glm_result
	GLM result structure. More...
struct	group_result
	Grouping result. More...
struct	hazard_rate_result
	Hazard rate result. More...
struct	is_random_engine
	Type trait to determine if a type is a random engine. More...
struct	is_random_engine< std::knuth_b >
	Specialization for std::knuth_b. More...
struct	is_random_engine< std::minstd_rand >
	Specialization for std::minstd_rand. More...
struct	is_random_engine< std::minstd_rand0 >
	Specialization for std::minstd_rand0. More...
struct	is_random_engine< std::mt19937 >
	Specialization for std::mt19937. More...
struct	is_random_engine< std::mt19937_64 >
	Specialization for std::mt19937_64. More...
struct	is_random_engine< std::ranlux24 >
	Specialization for std::ranlux24. More...
struct	is_random_engine< std::ranlux24_base >
	Specialization for std::ranlux24_base. More...
struct	is_random_engine< std::ranlux48 >
	Specialization for std::ranlux48. More...
struct	is_random_engine< std::ranlux48_base >
	Specialization for std::ranlux48_base. More...
struct	kaplan_meier_result
	Kaplan-Meier estimation result. More...
struct	kmeans_result
	K-means clustering result. More...
struct	label_encoding_result
	Label encoding result. More...
struct	logrank_result
	Log-rank test result. More...
struct	mcar_test_result
	Little's MCAR test result. More...
struct	missing_pattern_info
	Missing pattern information. More...
struct	multiple_imputation_result
	Multiple imputation result. More...
struct	multiple_regression_result
	Structure to store multiple regression analysis results. More...
struct	odds_ratio_result
	Odds ratio result. More...
struct	one_way_anova_result
	Structure storing one-way ANOVA results. More...
struct	outlier_detection_result
	Outlier detection result. More...
struct	pca_result
	PCA result. More...
struct	permutation_result
	Structure to store permutation test results. More...
struct	posthoc_comparison
	Structure storing individual pairwise comparison result in post-hoc tests. More...
struct	posthoc_result
	Structure storing post-hoc comparison results. More...
struct	power_result
	Power analysis result. More...
struct	prediction_interval
	Structure to store prediction interval results. More...
struct	quartile_result
	Quartile result. More...
struct	regularized_regression_result
	Structure to store regularized regression results. More...
struct	relative_risk_result
	Relative risk result. More...
struct	residual_diagnostics
	Structure to store residual diagnostics results. More...
struct	risk_difference_result
	Risk difference result. More...
struct	sensitivity_analysis_result
	Sensitivity analysis result (single parameter) More...
struct	simple_regression_result
	Structure to store simple regression analysis results. More...
struct	test_result
	Structure to store statistical test results. More...
struct	tipping_point_result
	Tipping point analysis result. More...
struct	two_way_anova_result
	Structure storing two-way ANOVA results. More...
struct	validation_result
	Data validation result. More...

Typedefs
using	default_random_engine = std::mt19937_64
	Default random engine type (Mersenne Twister 64-bit version)

Enumerations
enum class	linkage_type { single , complete , average , ward }
	Linkage types. More...
enum class	effect_size_magnitude { negligible , small , medium , large }
	Enumeration for effect size magnitude. More...
enum class	link_function {   identity , logit , probit , log ,   inverse , cloglog }
	Link function types. More...
enum class	distribution_family { gaussian , binomial , poisson , gamma_family }
	Distribution family. More...
enum class	missing_mechanism { mcar , mar , mnar , unknown }
	Missing mechanism types. More...
enum class	alternative_hypothesis { two_sided , less , greater }
	Enumeration representing the type of alternative hypothesis. More...

Functions
one_way_anova_result	one_way_anova (const std::vector< std::vector< double > > &groups)
	Perform one-way analysis of variance.
two_way_anova_result	two_way_anova (const std::vector< std::vector< std::vector< double > > > &data)
	Perform two-way analysis of variance (with replication)
posthoc_result	tukey_hsd (const one_way_anova_result &anova_result, const std::vector< std::vector< double > > &groups, double alpha=0.05)
	Perform Tukey's Honestly Significant Difference (HSD) test.
posthoc_result	bonferroni_posthoc (const one_way_anova_result &anova_result, double alpha=0.05)
	Perform Bonferroni method for multiple comparisons.
posthoc_result	dunnett_posthoc (const one_way_anova_result &anova_result, std::size_t control_group=0, double alpha=0.05)
	Perform Dunnett's test for multiple comparisons against a control group.
posthoc_result	scheffe_posthoc (const one_way_anova_result &anova_result, double alpha=0.05)
	Perform Scheffe's method for multiple comparisons.
ancova_result	one_way_ancova (const std::vector< std::vector< std::pair< double, double > > > &groups)
	Perform one-way analysis of covariance.
double	eta_squared (const one_way_anova_result &result)
	Calculate Eta-squared for one-way ANOVA.
double	partial_eta_squared_a (const two_way_anova_result &result)
	Calculate Partial eta-squared for factor A in two-way ANOVA.
double	partial_eta_squared_b (const two_way_anova_result &result)
	Calculate Partial eta-squared for factor B in two-way ANOVA.
double	partial_eta_squared_interaction (const two_way_anova_result &result)
	Calculate Partial eta-squared for interaction in two-way ANOVA.
double	omega_squared (const one_way_anova_result &result)
	Calculate Omega-squared for one-way ANOVA.
double	cohens_f (const one_way_anova_result &result)
	Calculate Cohen's f for one-way ANOVA.
template<typename Iterator >
auto	sum (Iterator first, Iterator last)
	Sum.
template<typename Iterator , typename Projection >
auto	sum (Iterator first, Iterator last, Projection proj)
	Sum of projected values using a lambda expression.
template<typename Iterator >
std::size_t	count (Iterator first, Iterator last)
	Data count.
template<typename Iterator >
double	mean (Iterator first, Iterator last)
	Arithmetic mean.
template<typename Iterator , typename Projection >
double	mean (Iterator first, Iterator last, Projection proj)
	Arithmetic mean of projected values using a lambda expression.
template<typename Iterator >
double	median (Iterator first, Iterator last)
	Median (accepts a sorted range)
template<typename Iterator , typename Projection >
double	median (Iterator first, Iterator last, Projection proj)
	Median of projected values using a lambda expression (projection results must be in sorted order)
template<typename Iterator >
auto	mode (Iterator first, Iterator last)
	Mode (returns the smallest value when there are multiple modes: guarantees deterministic behavior)
template<typename Iterator , typename Projection >
auto	mode (Iterator first, Iterator last, Projection proj)
	Mode of projected values using a lambda expression.
template<typename Iterator >
auto	modes (Iterator first, Iterator last) -> std::vector< typename std::iterator_traits< Iterator >::value_type >
	Returns all modes (returns a vector sorted in ascending order)
template<typename Iterator , typename Projection >
auto	modes (Iterator first, Iterator last, Projection proj) -> std::vector< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type > >
	Returns all modes of projected values using a lambda expression.
template<typename Iterator >
double	geometric_mean (Iterator first, Iterator last)
	Geometric mean.
template<typename Iterator , typename Projection >
double	geometric_mean (Iterator first, Iterator last, Projection proj)
	Geometric mean of projected values using a lambda expression.
template<typename Iterator >
double	harmonic_mean (Iterator first, Iterator last)
	Harmonic mean.
template<typename Iterator , typename Projection >
double	harmonic_mean (Iterator first, Iterator last, Projection proj)
	Harmonic mean of projected values using a lambda expression.
template<typename Iterator >
double	trimmed_mean (Iterator first, Iterator last, double proportion)
	Trimmed mean (accepts a sorted range. proportion: exclusion ratio per side, 0.0 to less than 0.5)
template<typename Iterator , typename Projection >
double	trimmed_mean (Iterator first, Iterator last, double proportion, Projection proj)
	Trimmed mean of projected values using a lambda expression (projection results must be in sorted order)
template<typename Iterator , typename WeightIterator >
double	weighted_mean (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last)
	Weighted mean.
template<typename Iterator , typename WeightIterator >
double	weighted_mean (Iterator first, Iterator last, WeightIterator weight_first)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_mean (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, Projection proj)
	Weighted mean (projection version)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_mean (Iterator first, Iterator last, WeightIterator weight_first, Projection proj)
template<typename T1 , typename T2 >
double	logarithmic_mean (T1 a, T2 b)
	Logarithmic Mean.
template<typename Iterator , typename WeightIterator >
double	weighted_harmonic_mean (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last)
	Weighted harmonic mean (safe range version)
template<typename Iterator , typename WeightIterator >
double	weighted_harmonic_mean (Iterator first, Iterator last, WeightIterator weight_first)
	Weighted harmonic mean.
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_harmonic_mean (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, Projection proj)
	Weighted harmonic mean (safe range version with projection)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_harmonic_mean (Iterator first, Iterator last, WeightIterator weight_first, Projection proj)
	Weighted harmonic mean (projection version)
template<typename Iterator >
std::size_t	argmin (Iterator first, Iterator last)
	Returns the index of the minimum value.
template<typename Iterator , typename Projection >
std::size_t	argmin (Iterator first, Iterator last, Projection proj)
	Returns the index of the minimum value (projection version)
template<typename Iterator >
std::size_t	argmax (Iterator first, Iterator last)
	Returns the index of the maximum value.
template<typename Iterator , typename Projection >
std::size_t	argmax (Iterator first, Iterator last, Projection proj)
	Returns the index of the maximum value (projection version)
contingency_table_result	contingency_table (const std::vector< std::size_t > &row_data, const std::vector< std::size_t > &col_data)
	Create a contingency table.
odds_ratio_result	odds_ratio (const std::vector< std::vector< std::size_t > > &table)
	Calculate odds ratio from a 2x2 contingency table.
odds_ratio_result	odds_ratio (std::size_t a, std::size_t b, std::size_t c, std::size_t d)
	Calculate odds ratio from a 2x2 contingency table (specifying cell values directly)
relative_risk_result	relative_risk (const std::vector< std::vector< std::size_t > > &table)
	Calculate relative risk (risk ratio) from a 2x2 contingency table.
relative_risk_result	relative_risk (std::size_t a, std::size_t b, std::size_t c, std::size_t d)
	Calculate relative risk from a 2x2 contingency table (specifying cell values directly)
risk_difference_result	risk_difference (const std::vector< std::vector< std::size_t > > &table)
	Calculate risk difference from a 2x2 contingency table.
risk_difference_result	risk_difference (std::size_t a, std::size_t b, std::size_t c, std::size_t d)
	Calculate risk difference from a 2x2 contingency table (specifying cell values directly)
double	number_needed_to_treat (const std::vector< std::vector< std::size_t > > &table)
	Calculate Number Needed to Treat (NNT)
double	euclidean_distance (const std::vector< double > &a, const std::vector< double > &b)
	Euclidean distance.
double	manhattan_distance (const std::vector< double > &a, const std::vector< double > &b)
	Manhattan distance.
std::vector< std::vector< double > >	kmeans_plusplus_init (const std::vector< std::vector< double > > &data, std::size_t k)
	K-means++ initialization.
kmeans_result	kmeans (const std::vector< std::vector< double > > &data, std::size_t k, std::size_t max_iter=100, double tol=1e-6)
	K-means clustering.
std::vector< dendrogram_node >	hierarchical_clustering (const std::vector< std::vector< double > > &data, linkage_type linkage=linkage_type::single)
	Hierarchical clustering.
std::vector< std::size_t >	cut_dendrogram (const std::vector< dendrogram_node > &dendrogram, std::size_t n_data, std::size_t k)
	Extract k clusters from dendrogram.
double	silhouette_score (const std::vector< std::vector< double > > &data, const std::vector< std::size_t > &labels)
	Calculate silhouette score.
double	uniform_pdf (double x, double a=0.0, double b=1.0)
	Uniform distribution probability density function (PDF)
double	uniform_cdf (double x, double a=0.0, double b=1.0)
	Uniform distribution cumulative distribution function (CDF)
double	uniform_quantile (double p, double a=0.0, double b=1.0)
	Uniform distribution quantile function (inverse CDF)
template<typename Engine = default_random_engine>
double	uniform_rand (double a, double b, Engine &engine)
	Uniform distribution random number generation.
double	uniform_rand (double a=0.0, double b=1.0)
	Uniform distribution random number generation (using default engine)
double	normal_pdf (double x, double mu=0.0, double sigma=1.0)
	Normal distribution probability density function (PDF)
double	normal_cdf (double x, double mu=0.0, double sigma=1.0)
	Normal distribution cumulative distribution function (CDF)
double	normal_quantile (double p, double mu=0.0, double sigma=1.0)
	Normal distribution quantile function (inverse CDF, percent point function)
template<typename Engine = default_random_engine>
double	normal_rand (double mu, double sigma, Engine &engine)
	Normal distribution random number generation.
double	normal_rand (double mu=0.0, double sigma=1.0)
	Normal distribution random number generation (using default engine)
double	exponential_pdf (double x, double lambda=1.0)
	Exponential distribution probability density function (PDF)
double	exponential_cdf (double x, double lambda=1.0)
	Exponential distribution cumulative distribution function (CDF)
double	exponential_quantile (double p, double lambda=1.0)
	Exponential distribution quantile function.
template<typename Engine = default_random_engine>
double	exponential_rand (double lambda, Engine &engine)
	Exponential distribution random number generation.
double	exponential_rand (double lambda=1.0)
	Exponential distribution random number generation (using default engine)
double	gamma_pdf (double x, double shape, double rate=1.0)
	Gamma distribution probability density function (PDF)
double	gamma_cdf (double x, double shape, double rate=1.0)
	Gamma distribution cumulative distribution function (CDF)
double	gamma_quantile (double p, double shape, double rate=1.0)
	Gamma distribution quantile function.
template<typename Engine = default_random_engine>
double	gamma_rand (double shape, double rate, Engine &engine)
	Gamma distribution random number generation.
double	gamma_rand (double shape, double rate=1.0)
	Gamma distribution random number generation (using default engine)
double	beta_pdf (double x, double alpha, double beta_param)
	Beta distribution probability density function (PDF)
double	beta_cdf (double x, double alpha, double beta_param)
	Beta distribution cumulative distribution function (CDF)
double	beta_quantile (double p, double alpha, double beta_param)
	Beta distribution quantile function.
template<typename Engine = default_random_engine>
double	beta_rand (double alpha, double beta_param, Engine &engine)
	Beta distribution random number generation (using gamma variates)
double	beta_rand (double alpha, double beta_param)
	Beta distribution random number generation (using default engine)
double	chisq_pdf (double x, double df)
	Chi-square distribution probability density function (PDF)
double	chisq_cdf (double x, double df)
	Chi-square distribution cumulative distribution function (CDF)
double	chisq_quantile (double p, double df)
	Chi-square distribution quantile function.
template<typename Engine = default_random_engine>
double	chisq_rand (double df, Engine &engine)
	Chi-square distribution random number generation.
double	chisq_rand (double df)
	Chi-square distribution random number generation (using default engine)
double	t_pdf (double x, double df)
	t-distribution probability density function (PDF)
double	t_cdf (double x, double df)
	t-distribution cumulative distribution function (CDF)
double	t_quantile (double p, double df)
	t-distribution quantile function (Newton-Raphson method)
template<typename Engine = default_random_engine>
double	t_rand (double df, Engine &engine)
	t-distribution random number generation
double	t_rand (double df)
	t-distribution random number generation (using default engine)
double	f_pdf (double x, double df1, double df2)
	F-distribution probability density function (PDF)
double	f_cdf (double x, double df1, double df2)
	F-distribution cumulative distribution function (CDF)
double	f_quantile (double p, double df1, double df2)
	F-distribution quantile function (Newton-Raphson method)
template<typename Engine = default_random_engine>
double	f_rand (double df1, double df2, Engine &engine)
	F-distribution random number generation.
double	f_rand (double df1, double df2)
	F-distribution random number generation (using default engine)
double	lognormal_pdf (double x, double mu=0.0, double sigma=1.0)
	Log-normal distribution probability density function (PDF)
double	lognormal_cdf (double x, double mu=0.0, double sigma=1.0)
	Log-normal distribution cumulative distribution function (CDF)
double	lognormal_quantile (double p, double mu=0.0, double sigma=1.0)
	Log-normal distribution quantile function.
template<typename Engine = default_random_engine>
double	lognormal_rand (double mu, double sigma, Engine &engine)
	Log-normal distribution random number generation.
double	lognormal_rand (double mu=0.0, double sigma=1.0)
	Log-normal distribution random number generation (using default engine)
double	weibull_pdf (double x, double shape, double scale=1.0)
	Weibull distribution probability density function (PDF)
double	weibull_cdf (double x, double shape, double scale=1.0)
	Weibull distribution cumulative distribution function (CDF)
double	weibull_quantile (double p, double shape, double scale=1.0)
	Weibull distribution quantile function.
template<typename Engine = default_random_engine>
double	weibull_rand (double shape, double scale, Engine &engine)
	Weibull distribution random number generation.
double	weibull_rand (double shape, double scale=1.0)
	Weibull distribution random number generation (using default engine)
double	studentized_range_cdf (double q, double k, double df)
	CDF of the studentized range distribution.
double	studentized_range_quantile (double p, double k, double df)
	Quantile function of the studentized range distribution.
template<typename Iterator1 , typename Iterator2 >
double	population_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Population covariance.
template<typename Iterator1 , typename Iterator2 >
double	population_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double mean_x, double mean_y)
	Population covariance with precomputed means.
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	population_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Population covariance (projection version)
template<typename Iterator1 , typename Iterator2 >
double	sample_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Sample covariance (unbiased covariance)
template<typename Iterator1 , typename Iterator2 >
double	sample_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double mean_x, double mean_y)
	Sample covariance with precomputed means.
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	sample_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Sample covariance (projection version)
template<typename Iterator1 , typename Iterator2 >
double	covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Covariance (alias for sample_covariance)
template<typename Iterator1 , typename Iterator2 >
double	covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double mean_x, double mean_y)
	Covariance with precomputed means (alias for sample_covariance)
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Covariance (projection version, alias for sample_covariance)
template<typename Iterator1 , typename Iterator2 >
double	pearson_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Pearson correlation coefficient.
template<typename Iterator1 , typename Iterator2 >
double	pearson_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double mean_x, double mean_y)
	Pearson correlation coefficient with precomputed means.
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	pearson_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Pearson correlation coefficient (projection version)
template<typename Iterator1 , typename Iterator2 >
double	spearman_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Spearman's rank correlation coefficient.
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	spearman_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Spearman's rank correlation coefficient (projection version)
template<typename Iterator1 , typename Iterator2 >
double	kendall_tau (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Kendall's rank correlation coefficient (tau-b)
template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >
double	kendall_tau (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Projection1 proj1, Projection2 proj2)
	Kendall's rank correlation coefficient (projection version)
template<typename Iterator1 , typename Iterator2 , typename WeightIterator >
double	weighted_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, WeightIterator weight_first)
	Weighted covariance.
template<typename Iterator1 , typename Iterator2 , typename WeightIterator , typename Projection1 , typename Projection2 >
double	weighted_covariance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, WeightIterator weight_first, Projection1 proj1, Projection2 proj2)
	Weighted covariance (projection version)
bool	is_na (double x)
	Check if a value is NA.
template<typename T >
std::vector< std::vector< T > >	dropna (const std::vector< std::vector< T > > &data)
	Drop rows containing NA.
template<typename T >
std::vector< T >	dropna (const std::vector< T > &data)
	Drop NA from a 1-dimensional vector.
template<typename T >
std::vector< T >	fillna (const std::vector< T > &data, T fill_value)
	Fill NA with a specified value.
std::vector< double >	fillna_mean (const std::vector< double > &data)
	Fill NA with mean.
std::vector< double >	fillna_median (const std::vector< double > &data)
	Fill NA with median.
std::vector< double >	fillna_ffill (const std::vector< double > &data)
	Fill NA with forward fill.
std::vector< double >	fillna_bfill (const std::vector< double > &data)
	Fill NA with backward fill.
std::vector< double >	fillna_interpolate (const std::vector< double > &data)
	Fill NA with linear interpolation.
template<typename T , typename Predicate >
std::vector< T >	filter (const std::vector< T > &data, Predicate pred)
	Filter elements that match a condition.
template<typename T , typename Predicate >
std::vector< std::vector< T > >	filter_rows (const std::vector< std::vector< T > > &data, Predicate pred)
	Filter rows that match a condition (2-dimensional)
template<typename T >
std::vector< T >	filter_range (const std::vector< T > &data, T min_val, T max_val)
	Filter values within a range.
std::vector< double >	log_transform (const std::vector< double > &data)
	Logarithmic transformation (natural logarithm)
std::vector< double >	log1p_transform (const std::vector< double > &data)
	Logarithmic transformation (log1p: log(1 + x))
std::vector< double >	sqrt_transform (const std::vector< double > &data)
	Square root transformation.
std::vector< double >	boxcox_transform (const std::vector< double > &data, double lambda)
	Box-Cox transformation.
std::vector< double >	rank_transform (const std::vector< double > &data)
	Rank transformation.
template<typename K , typename V >
group_result< K, V >	group_by (const std::vector< K > &keys, const std::vector< V > &values)
	Group by.
template<typename K >
aggregation_result< K >	group_mean (const std::vector< K > &keys, const std::vector< double > &values)
	Mean per group.
template<typename K >
aggregation_result< K >	group_sum (const std::vector< K > &keys, const std::vector< double > &values)
	Sum per group.
template<typename K >
aggregation_result< K >	group_count (const std::vector< K > &keys, const std::vector< double > &values)
	Count per group.
template<typename T >
std::vector< T >	sort_values (const std::vector< T > &data, bool ascending=true)
	Return a sorted vector (ascending)
template<typename T >
std::vector< std::size_t >	argsort (const std::vector< T > &data, bool ascending=true)
	Return indices in sorted order.
template<typename T >
std::vector< T >	sample_with_replacement (const std::vector< T > &data, std::size_t n)
	Random sampling (with replacement)
template<typename T >
std::vector< T >	sample_without_replacement (const std::vector< T > &data, std::size_t n)
	Random sampling (without replacement)
template<typename K , typename V >
std::vector< V >	stratified_sample (const std::vector< K > &strata, const std::vector< V > &data, double sample_ratio)
	Stratified sampling.
template<typename T >
std::vector< T >	drop_duplicates (const std::vector< T > &data)
	Drop duplicates.
template<typename T >
std::map< T, std::size_t >	value_counts (const std::vector< T > &data)
	Count duplicates.
template<typename T >
std::vector< T >	get_duplicates (const std::vector< T > &data)
	Get duplicate values.
std::vector< double >	rolling_mean (const std::vector< double > &data, std::size_t window)
	Moving average.
std::vector< double >	rolling_std (const std::vector< double > &data, std::size_t window)
	Moving standard deviation.
std::vector< double >	rolling_min (const std::vector< double > &data, std::size_t window)
	Moving minimum.
std::vector< double >	rolling_max (const std::vector< double > &data, std::size_t window)
	Moving maximum.
std::vector< double >	rolling_sum (const std::vector< double > &data, std::size_t window)
	Moving sum.
template<typename T >
label_encoding_result< T >	label_encode (const std::vector< T > &data)
	Label encoding.
template<typename T >
std::vector< std::vector< double > >	one_hot_encode (const std::vector< T > &data)
	One-hot encoding.
std::vector< std::size_t >	bin_equal_width (const std::vector< double > &data, std::size_t n_bins)
	Binning (equal width)
std::vector< std::size_t >	bin_equal_freq (const std::vector< double > &data, std::size_t n_bins)
	Binning (equal frequency)
validation_result	validate_data (const std::vector< double > &data, bool allow_missing=false, bool allow_infinite=false, bool allow_negative=true)
	Data validation.
bool	validate_range (const std::vector< double > &data, double min_val=-std::numeric_limits< double >::infinity(), double max_val=std::numeric_limits< double >::infinity())
	Range validation.
double	log_factorial (std::uint64_t n)
	Calculate log factorial.
double	log_binomial_coef (std::uint64_t n, std::uint64_t k)
	Calculate log binomial coefficient.
double	binomial_coef (std::uint64_t n, std::uint64_t k)
	Calculate binomial coefficient.
double	binomial_pmf (std::uint64_t k, std::uint64_t n, double p)
	Binomial distribution probability mass function (PMF)
double	binomial_cdf (std::uint64_t k, std::uint64_t n, double p)
	Binomial distribution cumulative distribution function (CDF)
std::uint64_t	binomial_quantile (double prob, std::uint64_t n, double p)
	Binomial distribution quantile function.
template<typename Engine = default_random_engine>
std::uint64_t	binomial_rand (std::uint64_t n, double p, Engine &engine)
	Binomial distribution random number generation.
std::uint64_t	binomial_rand (std::uint64_t n, double p)
	Binomial distribution random number generation (using default engine)
double	poisson_pmf (std::uint64_t k, double lambda)
	Poisson distribution probability mass function (PMF)
double	poisson_cdf (std::uint64_t k, double lambda)
	Poisson distribution cumulative distribution function (CDF)
std::uint64_t	poisson_quantile (double p, double lambda)
	Poisson distribution quantile function.
template<typename Engine = default_random_engine>
std::uint64_t	poisson_rand (double lambda, Engine &engine)
	Poisson distribution random number generation.
std::uint64_t	poisson_rand (double lambda)
	Poisson distribution random number generation (using default engine)
double	geometric_pmf (std::uint64_t k, double p)
	Geometric distribution probability mass function (PMF)
double	geometric_cdf (std::uint64_t k, double p)
	Geometric distribution cumulative distribution function (CDF)
std::uint64_t	geometric_quantile (double prob, double p)
	Geometric distribution quantile function (inverse CDF)
template<typename Engine = default_random_engine>
std::uint64_t	geometric_rand (double p, Engine &engine)
	Geometric distribution random number generation.
std::uint64_t	geometric_rand (double p)
	Geometric distribution random number generation (using default engine)
double	hypergeom_pmf (std::uint64_t k, std::uint64_t N, std::uint64_t K, std::uint64_t n)
	Hypergeometric distribution probability mass function (PMF)
double	hypergeom_cdf (std::uint64_t k, std::uint64_t N, std::uint64_t K, std::uint64_t n)
	Hypergeometric distribution cumulative distribution function (CDF)
std::uint64_t	hypergeom_quantile (double p, std::uint64_t N, std::uint64_t K, std::uint64_t n)
	Hypergeometric distribution quantile function (inverse CDF)
template<typename Engine = default_random_engine>
std::uint64_t	hypergeom_rand (std::uint64_t N, std::uint64_t K, std::uint64_t n, Engine &engine)
	Hypergeometric distribution random number generation.
std::uint64_t	hypergeom_rand (std::uint64_t N, std::uint64_t K, std::uint64_t n)
	Hypergeometric distribution random number generation (using default engine)
double	nbinom_pmf (std::uint64_t k, double r, double p)
	Negative binomial distribution probability mass function (PMF)
double	nbinom_cdf (std::uint64_t k, double r, double p)
	Negative binomial distribution cumulative distribution function (CDF)
std::uint64_t	nbinom_quantile (double prob, double r, double p)
	Negative binomial distribution quantile function (inverse CDF)
template<typename Engine = default_random_engine>
std::uint64_t	nbinom_rand (double r, double p, Engine &engine)
	Negative binomial distribution random number generation.
std::uint64_t	nbinom_rand (double r, double p)
	Negative binomial distribution random number generation (using default engine)
double	bernoulli_pmf (std::uint64_t k, double p)
	Bernoulli distribution probability mass function (PMF)
double	bernoulli_cdf (std::uint64_t k, double p)
	Bernoulli distribution cumulative distribution function (CDF)
std::uint64_t	bernoulli_quantile (double prob, double p)
	Bernoulli distribution quantile function.
template<typename Engine = default_random_engine>
std::uint64_t	bernoulli_rand (double p, Engine &engine)
	Bernoulli distribution random number generation.
std::uint64_t	bernoulli_rand (double p)
	Bernoulli distribution random number generation (using default engine)
double	discrete_uniform_pmf (std::int64_t k, std::int64_t a, std::int64_t b)
	Discrete uniform distribution probability mass function (PMF)
double	discrete_uniform_cdf (std::int64_t k, std::int64_t a, std::int64_t b)
	Discrete uniform distribution cumulative distribution function (CDF)
std::int64_t	discrete_uniform_quantile (double p, std::int64_t a, std::int64_t b)
	Discrete uniform distribution quantile function.
template<typename Engine = default_random_engine>
std::int64_t	discrete_uniform_rand (std::int64_t a, std::int64_t b, Engine &engine)
	Discrete uniform distribution random number generation.
std::int64_t	discrete_uniform_rand (std::int64_t a, std::int64_t b)
	Discrete uniform distribution random number generation (using default engine)
template<typename Iterator >
double	range (Iterator first, Iterator last)
	Range (maximum - minimum)
template<typename Iterator , typename Projection >
double	range (Iterator first, Iterator last, Projection proj)
	Range of projected values using a lambda expression.
template<typename Iterator >
double	var (Iterator first, Iterator last, std::size_t ddof=0)
	Variance (ddof = Delta Degrees of Freedom)
template<typename Iterator >
double	var (Iterator first, Iterator last, double precomputed_mean, std::size_t ddof)
	Variance using precomputed mean (with ddof)
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	var (Iterator first, Iterator last, Projection proj, std::size_t ddof=0)
	Variance of projected values using a lambda expression (with ddof)
template<typename Iterator , typename Projection >
double	var (Iterator first, Iterator last, Projection proj, double precomputed_mean, std::size_t ddof)
	Variance of projected values using precomputed mean (with ddof)
template<typename Iterator >
double	population_variance (Iterator first, Iterator last)
	Population variance.
template<typename Iterator >
double	population_variance (Iterator first, Iterator last, double precomputed_mean)
	Population variance using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	population_variance (Iterator first, Iterator last, Projection proj)
	Population variance of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	population_variance (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Population variance of projected values using precomputed mean.
template<typename Iterator >
double	sample_variance (Iterator first, Iterator last)
	Sample variance (unbiased variance)
template<typename Iterator >
double	sample_variance (Iterator first, Iterator last, double precomputed_mean)
	Sample variance using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	sample_variance (Iterator first, Iterator last, Projection proj)
	Sample variance of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	sample_variance (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Sample variance of projected values using precomputed mean.
template<typename Iterator >
double	variance (Iterator first, Iterator last)
	Variance (alias for sample_variance)
template<typename Iterator >
double	variance (Iterator first, Iterator last, double precomputed_mean)
	Variance using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	variance (Iterator first, Iterator last, Projection proj)
	Variance of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	variance (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Variance of projected values using precomputed mean.
template<typename Iterator >
double	stdev (Iterator first, Iterator last, std::size_t ddof=0)
	Standard deviation (ddof = Delta Degrees of Freedom)
template<typename Iterator >
double	stdev (Iterator first, Iterator last, double precomputed_mean, std::size_t ddof)
	Standard deviation using precomputed mean (with ddof)
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	stdev (Iterator first, Iterator last, Projection proj, std::size_t ddof=0)
	Standard deviation of projected values using a lambda expression (with ddof)
template<typename Iterator , typename Projection >
double	stdev (Iterator first, Iterator last, Projection proj, double precomputed_mean, std::size_t ddof)
	Standard deviation of projected values using precomputed mean (with ddof)
template<typename Iterator >
double	population_stddev (Iterator first, Iterator last)
	Population standard deviation.
template<typename Iterator >
double	population_stddev (Iterator first, Iterator last, double precomputed_mean)
	Population standard deviation using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	population_stddev (Iterator first, Iterator last, Projection proj)
	Population standard deviation of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	population_stddev (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Population standard deviation of projected values using precomputed mean.
template<typename Iterator >
double	sample_stddev (Iterator first, Iterator last)
	Sample standard deviation.
template<typename Iterator >
double	sample_stddev (Iterator first, Iterator last, double precomputed_mean)
	Sample standard deviation using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	sample_stddev (Iterator first, Iterator last, Projection proj)
	Sample standard deviation of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	sample_stddev (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Sample standard deviation of projected values using precomputed mean.
template<typename Iterator >
double	stddev (Iterator first, Iterator last)
	Standard deviation (alias for sample_stddev)
template<typename Iterator >
double	stddev (Iterator first, Iterator last, double precomputed_mean)
	Standard deviation using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	stddev (Iterator first, Iterator last, Projection proj)
	Standard deviation of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	stddev (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Standard deviation of projected values using precomputed mean.
template<typename Iterator >
double	coefficient_of_variation (Iterator first, Iterator last)
	Coefficient of variation.
template<typename Iterator >
double	coefficient_of_variation (Iterator first, Iterator last, double precomputed_mean)
	Coefficient of variation using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	coefficient_of_variation (Iterator first, Iterator last, Projection proj)
	Coefficient of variation of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	coefficient_of_variation (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Coefficient of variation of projected values using precomputed mean.
template<typename Iterator >
double	iqr (Iterator first, Iterator last)
	Interquartile range (accepts a sorted range)
template<typename Iterator , typename Projection >
double	iqr (Iterator first, Iterator last, Projection proj)
	Interquartile range of projected values (projection results must be in sorted order)
template<typename Iterator >
double	mean_absolute_deviation (Iterator first, Iterator last)
	Mean absolute deviation.
template<typename Iterator >
double	mean_absolute_deviation (Iterator first, Iterator last, double precomputed_mean)
	Mean absolute deviation using precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	mean_absolute_deviation (Iterator first, Iterator last, Projection proj)
	Mean absolute deviation of projected values using a lambda expression.
template<typename Iterator , typename Projection >
double	mean_absolute_deviation (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Mean absolute deviation of projected values using precomputed mean.
template<typename Iterator , typename WeightIterator >
double	weighted_variance (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last)
	Weighted variance (reliability weights / analytic weights)
template<typename Iterator , typename WeightIterator >
double	weighted_variance (Iterator first, Iterator last, WeightIterator weight_first)
	Weighted variance (reliability weights / analytic weights)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_variance (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, Projection proj)
	Weighted variance (projection version)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_variance (Iterator first, Iterator last, WeightIterator weight_first, Projection proj)
	Weighted variance (projection version)
template<typename Iterator , typename WeightIterator >
double	weighted_stddev (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last)
	Weighted standard deviation.
template<typename Iterator , typename WeightIterator >
double	weighted_stddev (Iterator first, Iterator last, WeightIterator weight_first)
	Weighted standard deviation.
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_stddev (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, Projection proj)
	Weighted standard deviation (projection version)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_stddev (Iterator first, Iterator last, WeightIterator weight_first, Projection proj)
	Weighted standard deviation (projection version)
template<typename Iterator >
double	geometric_stddev (Iterator first, Iterator last)
	Geometric standard deviation.
template<typename Iterator , typename Projection >
double	geometric_stddev (Iterator first, Iterator last, Projection proj)
	Geometric standard deviation (projection version)
template<typename Iterator1 , typename Iterator2 >
double	euclidean_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Euclidean distance (L2 norm)
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	euclidean_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Proj1 proj1, Proj2 proj2)
	Euclidean distance with projection.
template<typename Iterator1 , typename Iterator2 >
double	manhattan_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Manhattan distance (L1 norm, taxicab distance)
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	manhattan_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Proj1 proj1, Proj2 proj2)
	Manhattan distance with projection.
template<typename Iterator1 , typename Iterator2 >
double	cosine_similarity (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Cosine similarity.
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	cosine_similarity (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Proj1 proj1, Proj2 proj2)
	Cosine similarity with projection.
template<typename Iterator1 , typename Iterator2 >
double	cosine_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Cosine distance.
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	cosine_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Proj1 proj1, Proj2 proj2)
	Cosine distance with projection.
double	mahalanobis_distance (const std::vector< double > &x, const std::vector< double > &mean, const std::vector< std::vector< double > > &cov_matrix)
	Mahalanobis distance.
template<typename Iterator1 , typename Iterator2 >
double	minkowski_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double p)
	Minkowski distance (generalized Lp distance)
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	minkowski_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double p, Proj1 proj1, Proj2 proj2)
	Minkowski distance with projection.
template<typename Iterator1 , typename Iterator2 >
double	chebyshev_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Chebyshev distance (L∞ norm, maximum metric)
template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >
double	chebyshev_distance (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, Proj1 proj1, Proj2 proj2)
	Chebyshev distance with projection.
template<typename Iterator >
double	cohens_d (Iterator first, Iterator last, double mu0, double sigma)
	Cohen's d (one-sample, known population standard deviation)
template<typename Iterator >
double	cohens_d (Iterator first, Iterator last, double mu0)
	Cohen's d (one-sample, using sample standard deviation)
template<typename Iterator1 , typename Iterator2 >
double	cohens_d_two_sample (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Cohen's d (two-sample, pooled standard deviation)
double	hedges_correction_factor (double df)
	Hedges' bias correction factor J.
template<typename Iterator >
double	hedges_g (Iterator first, Iterator last, double mu0)
	Hedges' g (one-sample)
template<typename Iterator1 , typename Iterator2 >
double	hedges_g_two_sample (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2)
	Hedges' g (two-sample)
template<typename Iterator1 , typename Iterator2 >
double	glass_delta (Iterator1 control_first, Iterator1 control_last, Iterator2 treatment_first, Iterator2 treatment_last)
	Glass's Delta (using control group's standard deviation)
double	t_to_r (double t, double df)
	Convert t-value to correlation coefficient.
double	d_to_r (double d)
	Convert Cohen's d to correlation coefficient.
double	r_to_d (double r)
	Convert correlation coefficient to Cohen's d.
double	eta_squared (double ss_effect, double ss_total)
	Calculate eta-squared from F-test.
double	partial_eta_squared (double f, double df1, double df2)
	Calculate partial eta-squared from F-test.
double	omega_squared (double ss_effect, double ss_total, double ms_error, double df_effect)
	Omega-squared.
double	cohens_h (double p1, double p2)
	Cohen's h (effect size for difference between two proportions)
double	odds_ratio (double a, double b, double c, double d)
	Odds ratio.
double	risk_ratio (double a, double b, double c, double d)
	Relative risk (risk ratio)
effect_size_magnitude	interpret_cohens_d (double d)
	Interpret Cohen's d.
effect_size_magnitude	interpret_correlation (double r)
	Interpret correlation coefficient.
effect_size_magnitude	interpret_eta_squared (double eta2)
	Interpret eta-squared.
template<typename Iterator >
double	standard_error (Iterator first, Iterator last)
	Calculate standard error of the mean.
template<typename Iterator , typename Projection >
double	standard_error (Iterator first, Iterator last, Projection proj)
	Calculate standard error of the mean (projection version)
template<typename Iterator >
double	standard_error (Iterator first, Iterator last, double precomputed_stddev)
	Calculate standard error of the mean (using precomputed standard deviation)
template<typename Iterator >
confidence_interval	ci_mean (Iterator first, Iterator last, double confidence=0.95)
	Calculate confidence interval for mean (t-distribution based)
template<typename Iterator , typename Projection >
confidence_interval	ci_mean (Iterator first, Iterator last, double confidence, Projection proj)
	Calculate confidence interval for mean (projection version)
template<typename Iterator >
confidence_interval	ci_mean_z (Iterator first, Iterator last, double sigma, double confidence=0.95)
	Calculate confidence interval for mean (z-distribution based, known variance)
confidence_interval	ci_proportion (std::size_t successes, std::size_t trials, double confidence=0.95)
	Calculate confidence interval for proportion (Wald method)
confidence_interval	ci_proportion_wilson (std::size_t successes, std::size_t trials, double confidence=0.95)
	Calculate confidence interval for proportion (Wilson method, recommended)
template<typename Iterator >
confidence_interval	ci_variance (Iterator first, Iterator last, double confidence=0.95)
	Calculate confidence interval for variance (chi-square distribution based)
template<typename Iterator1 , typename Iterator2 >
confidence_interval	ci_mean_diff (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double confidence=0.95)
	Calculate confidence interval for difference of two-sample means (independent samples, pooled variance)
template<typename Iterator1 , typename Iterator2 >
confidence_interval	ci_mean_diff_welch (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double confidence=0.95)
	Calculate confidence interval for difference of two-sample means (Welch method, not assuming equal variances)
template<typename Iterator >
double	margin_of_error_mean (Iterator first, Iterator last, double confidence=0.95)
	Calculate margin of error for mean.
template<typename Iterator , typename Projection >
double	margin_of_error_mean (Iterator first, Iterator last, double confidence, Projection proj)
	Calculate margin of error for mean (projection version)
double	margin_of_error_proportion (std::size_t successes, std::size_t n, double confidence=0.95)
	Calculate margin of error for proportion.
double	margin_of_error_proportion_worst_case (std::size_t n, double confidence=0.95)
	Calculate worst-case margin of error for proportion.
std::size_t	sample_size_for_moe_proportion (double margin_of_error, double confidence_level=0.95, double p_estimate=0.5)
	Calculate sample size for proportion estimation.
std::size_t	sample_size_for_moe_mean (double margin_of_error, double sigma, double confidence_level=0.95)
	Calculate sample size for mean estimation (known population standard deviation)
template<typename Iterator1 , typename Iterator2 >
confidence_interval	ci_mean_diff_pooled (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double confidence=0.95)
	Calculate confidence interval for two-sample mean difference (assuming equal variances)
confidence_interval	ci_proportion_diff (std::size_t successes1, std::size_t n1, std::size_t successes2, std::size_t n2, double confidence=0.95)
	Calculate confidence interval for two-sample proportion difference.
template<typename Iterator >
auto	frequency_table (Iterator first, Iterator last) -> frequency_table_result< typename std::iterator_traits< Iterator >::value_type >
	Create frequency table (returned with sorted keys)
template<typename Iterator , typename Projection >
auto	frequency_table (Iterator first, Iterator last, Projection proj) -> frequency_table_result< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type > >
	Frequency table with projection.
template<typename Iterator >
auto	frequency_count (Iterator first, Iterator last) -> std::unordered_map< typename std::iterator_traits< Iterator >::value_type, std::size_t >
	Return frequency for each value (unordered_map version, fast)
template<typename Iterator , typename Projection >
auto	frequency_count (Iterator first, Iterator last, Projection proj) -> std::unordered_map< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type >, std::size_t >
	Frequency count with projection.
template<typename Iterator >
auto	relative_frequency (Iterator first, Iterator last) -> std::unordered_map< typename std::iterator_traits< Iterator >::value_type, double >
	Return relative frequency for each value.
template<typename Iterator , typename Projection >
auto	relative_frequency (Iterator first, Iterator last, Projection proj) -> std::unordered_map< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type >, double >
	Relative frequency with projection.
template<typename Iterator >
auto	cumulative_frequency (Iterator first, Iterator last) -> std::vector< std::pair< typename std::iterator_traits< Iterator >::value_type, std::size_t > >
	Return cumulative frequency (for sorted values)
template<typename Iterator , typename Projection >
auto	cumulative_frequency (Iterator first, Iterator last, Projection proj) -> std::vector< std::pair< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type >, std::size_t > >
	Cumulative frequency with projection.
template<typename Iterator >
auto	cumulative_relative_frequency (Iterator first, Iterator last) -> std::vector< std::pair< typename std::iterator_traits< Iterator >::value_type, double > >
	Return cumulative relative frequency (for sorted values)
template<typename Iterator , typename Projection >
auto	cumulative_relative_frequency (Iterator first, Iterator last, Projection proj) -> std::vector< std::pair< std::invoke_result_t< Projection, typename std::iterator_traits< Iterator >::value_type >, double > >
	Cumulative relative frequency with projection.
glm_result	glm_fit (const std::vector< std::vector< double > > &X, const std::vector< double > &y, distribution_family family=distribution_family::gaussian, link_function link=link_function::identity, std::size_t max_iter=100, double tol=1e-8)
	Fit a generalized linear model.
glm_result	logistic_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t max_iter=100, double tol=1e-8)
	Logistic regression.
double	predict_probability (const glm_result &model, const std::vector< double > &x)
	Probability prediction with logistic regression.
std::vector< double >	odds_ratios (const glm_result &model)
	Calculate odds ratios.
std::vector< std::pair< double, double > >	odds_ratios_ci (const glm_result &model, double confidence=0.95)
	Confidence intervals for odds ratios.
glm_result	poisson_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t max_iter=100, double tol=1e-8)
	Poisson regression.
double	predict_count (const glm_result &model, const std::vector< double > &x)
	Expected count prediction with Poisson regression.
std::vector< double >	incidence_rate_ratios (const glm_result &model)
	Calculate Incidence Rate Ratios.
glm_residuals	compute_glm_residuals (const glm_result &model, const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Calculate GLM residuals.
double	overdispersion_test (const glm_result &model, const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Overdispersion test (for Poisson regression)
double	pseudo_r_squared_mcfadden (const glm_result &model)
	McFadden's pseudo R-squared.
double	pseudo_r_squared_nagelkerke (const glm_result &model, const std::vector< double > &y, std::size_t n)
	Nagelkerke's pseudo R-squared.
template<typename IteratorX , typename IteratorY >
simple_regression_result	simple_linear_regression (IteratorX x_first, IteratorX x_last, IteratorY y_first, IteratorY y_last)
	Perform simple linear regression.
multiple_regression_result	multiple_linear_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Perform multiple linear regression.
double	predict (const simple_regression_result &model, double x)
	Make prediction using simple regression model.
double	predict (const multiple_regression_result &model, const std::vector< double > &x)
	Make prediction using multiple regression model.
template<typename IteratorX >
prediction_interval	prediction_interval_simple (const simple_regression_result &model, IteratorX x_first, IteratorX x_last, double x_new, double confidence=0.95)
	Calculate prediction interval for simple regression model.
template<typename IteratorX >
prediction_interval	confidence_interval_mean (const simple_regression_result &model, IteratorX x_first, IteratorX x_last, double x_new, double confidence=0.95)
	Calculate confidence interval for mean of simple regression model.
template<typename IteratorX , typename IteratorY >
residual_diagnostics	compute_residual_diagnostics (const simple_regression_result &model, IteratorX x_first, IteratorX x_last, IteratorY y_first, IteratorY y_last)
	Perform residual diagnostics for simple regression model.
residual_diagnostics	compute_residual_diagnostics (const multiple_regression_result &model, const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Perform residual diagnostics for multiple regression model.
std::vector< double >	compute_vif (const std::vector< std::vector< double > > &X)
	Calculate VIF (Variance Inflation Factor) for each predictor.
double	correlation_matrix_determinant (const std::vector< std::vector< double > > &X)
	Calculate determinant of correlation matrix.
double	multicollinearity_score (const std::vector< std::vector< double > > &X)
	Calculate multicollinearity score.
template<typename IteratorY , typename IteratorPred >
double	r_squared (IteratorY y_first, IteratorY y_last, IteratorPred pred_first, IteratorPred pred_last)
	Calculate coefficient of determination from observed and predicted values.
template<typename IteratorY , typename IteratorPred >
double	adjusted_r_squared (IteratorY y_first, IteratorY y_last, IteratorPred pred_first, IteratorPred pred_last, std::size_t num_predictors)
	Calculate adjusted coefficient of determination.
missing_pattern_info	analyze_missing_patterns (const std::vector< std::vector< double > > &data)
	Analyze missing patterns.
std::vector< std::vector< double > >	create_missing_indicator (const std::vector< std::vector< double > > &data)
	Create missing indicator variables.
mcar_test_result	test_mcar_simple (const std::vector< std::vector< double > > &data)
	Little's MCAR test (simplified version)
missing_mechanism	diagnose_missing_mechanism (const std::vector< std::vector< double > > &data)
	Simple diagnosis of missing mechanism.
std::vector< double >	impute_conditional_mean (const std::vector< std::vector< double > > &data, std::size_t target_col, const std::vector< std::size_t > &predictor_cols)
	Single imputation by conditional mean.
multiple_imputation_result	multiple_imputation_pmm (const std::vector< std::vector< double > > &data, std::size_t m=5, unsigned int seed=0)
	Multiple imputation (PMM: Predictive Mean Matching)
multiple_imputation_result	multiple_imputation_bootstrap (const std::vector< std::vector< double > > &data, std::size_t m=5, unsigned int seed=0)
	Multiple imputation (simplified Bootstrap EM method)
sensitivity_analysis_result	sensitivity_analysis_pattern_mixture (const std::vector< double > &data, const std::vector< double > &delta_values)
	Sensitivity analysis using pattern mixture model.
sensitivity_analysis_result	sensitivity_analysis_selection_model (const std::vector< double > &data, const std::vector< double > &phi_values)
	Sensitivity analysis using selection model.
tipping_point_result	find_tipping_point (const std::vector< double > &data, double threshold=0.0, double delta_min=-5.0, double delta_max=5.0, std::size_t n_points=100)
	Tipping point analysis.
complete_case_result	extract_complete_cases (const std::vector< std::vector< double > > &data)
	Extract complete cases.
std::vector< std::vector< double > >	correlation_matrix_pairwise (const std::vector< std::vector< double > > &data)
	Correlation matrix using available case analysis (pairwise deletion)
double	aic (double log_likelihood, std::size_t k)
	Calculate AIC (Akaike Information Criterion)
double	aic_linear (const simple_regression_result &model, std::size_t n)
	Calculate AIC from simple regression model.
double	aic_linear (const multiple_regression_result &model, std::size_t n)
	Calculate AIC from multiple regression model.
double	aicc (double log_likelihood, std::size_t n, std::size_t k)
	Calculate AICc (corrected AIC)
double	bic (double log_likelihood, std::size_t n, std::size_t k)
	Calculate BIC (Bayesian Information Criterion)
double	bic_linear (const simple_regression_result &model, std::size_t n)
	Calculate BIC from simple regression model.
double	bic_linear (const multiple_regression_result &model, std::size_t n)
	Calculate BIC from multiple regression model.
template<typename IteratorX , typename IteratorY >
double	press_statistic (IteratorX x_first, IteratorX x_last, IteratorY y_first, IteratorY y_last, const simple_regression_result &model)
	Calculate PRESS statistic.
std::vector< std::vector< std::size_t > >	create_cv_folds (std::size_t n, std::size_t k, bool shuffle=true)
	Generate indices for k-fold cross-validation.
cv_result	cross_validate_linear (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t k=5)
	Perform k-fold cross-validation for multiple regression model.
cv_result	loocv_linear (const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Perform leave-one-out cross-validation.
regularized_regression_result	ridge_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, double lambda, bool standardize=true, std::size_t max_iter=1000, double tol=1e-6)
	Perform Ridge regression (L2 regularization)
regularized_regression_result	lasso_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, double lambda, bool standardize=true, std::size_t max_iter=1000, double tol=1e-6)
	Perform Lasso regression (L1 regularization)
regularized_regression_result	elastic_net_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, double lambda, double alpha=0.5, bool standardize=true, std::size_t max_iter=1000, double tol=1e-6)
	Perform Elastic Net regression (L1 + L2 regularization)
std::pair< double, std::vector< double > >	cv_ridge (const std::vector< std::vector< double > > &X, const std::vector< double > &y, const std::vector< double > &lambda_grid, std::size_t k=5)
	Select optimal lambda for Ridge regression using cross-validation.
std::pair< double, std::vector< double > >	cv_lasso (const std::vector< std::vector< double > > &X, const std::vector< double > &y, const std::vector< double > &lambda_grid, std::size_t k=5)
	Select optimal lambda for Lasso regression using cross-validation.
std::vector< double >	generate_lambda_grid (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t n_lambda=100, double lambda_min_ratio=0.0001)
	Automatically generate lambda grid for regularized regression.
std::vector< std::vector< double > >	covariance_matrix (const std::vector< std::vector< double > > &data)
	Calculate sample covariance matrix.
std::vector< std::vector< double > >	correlation_matrix (const std::vector< std::vector< double > > &data)
	Calculate Pearson correlation matrix.
std::vector< std::vector< double > >	standardize (const std::vector< std::vector< double > > &data)
	Z-score standardization.
std::vector< std::vector< double > >	min_max_scale (const std::vector< std::vector< double > > &data)
	Min-Max normalization (0-1 scaling)
std::pair< double, std::vector< double > >	power_iteration (const std::vector< std::vector< double > > &matrix, std::size_t max_iter=1000, double tol=1e-10)
	Find largest eigenvalue and eigenvector using power iteration.
pca_result	pca (const std::vector< std::vector< double > > &data, std::size_t n_components)
	Principal Component Analysis.
std::vector< std::vector< double > >	pca_transform (const std::vector< std::vector< double > > &data, const pca_result &pca)
	Project data onto principal component space.
template<typename Iterator >
std::vector< double >	compute_ranks_with_ties (Iterator first, Iterator last)
	Compute ranks with tie handling.
std::vector< std::size_t >	compute_tie_groups (const std::vector< double > &sorted_values)
	Compute tie group sizes from sorted data.
template<typename Iterator >
test_result	shapiro_wilk_test (Iterator first, Iterator last)
	Perform Shapiro-Wilk test.
template<typename Iterator >
test_result	lilliefors_test (Iterator first, Iterator last)
	Perform Lilliefors test for normality.
template<typename Iterator >
test_result	ks_test_normal (Iterator first, Iterator last)
	Perform Kolmogorov-Smirnov test for normality (deprecated)
test_result	levene_test (const std::vector< std::vector< double > > &groups)
	Perform Levene test (homogeneity of variance test)
test_result	bartlett_test (const std::vector< std::vector< double > > &groups)
	Perform Bartlett test (homogeneity of variance test)
template<typename Iterator >
test_result	wilcoxon_signed_rank_test (Iterator first, Iterator last, double mu0=0.0, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Perform Wilcoxon signed-rank test (one-sample)
template<typename Iterator1 , typename Iterator2 >
test_result	mann_whitney_u_test (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, alternative_hypothesis alt=alternative_hypothesis::two_sided, bool correct=true)
	Perform Mann-Whitney U test (two-sample)
test_result	kruskal_wallis_test (const std::vector< std::vector< double > > &groups)
	Perform Kruskal-Wallis test (k-sample)
test_result	fisher_exact_test (std::uint64_t a, std::uint64_t b, std::uint64_t c, std::uint64_t d, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Perform Fisher's exact test (2x2 contingency table)
bool	approx_equal (double a, double b, double rel_tol=default_rel_tol, double abs_tol=default_abs_tol)
	Check if two floating-point numbers are approximately equal.
bool	is_zero (double x, double tol=default_abs_tol)
	Check if a value is close to zero.
bool	is_finite (double x)
	Check if a value is finite (not infinity or NaN)
template<typename Iterator >
bool	all_finite (Iterator first, Iterator last)
	Check if all values in a range are finite.
bool	has_converged_abs (double x_new, double x_old, double tol=1e-6)
	Check for convergence based on absolute change.
bool	has_converged_rel (double x_new, double x_old, double tol=1e-6)
	Check for convergence based on relative change.
bool	has_converged (double x_new, double x_old, double abs_tol=1e-8, double rel_tol=1e-6)
	Check for convergence using combined absolute and relative criteria.
double	log1p_safe (double x)
	Safely compute log(1 + x) for small x.
double	expm1_safe (double x)
	Safely compute exp(x) - 1 for small x.
double	clamp (double x, double min_val, double max_val)
	Clamp a value to a range [min_val, max_val].
bool	in_range (double x, double min_val, double max_val)
	Check if a value is in range [min_val, max_val].
double	relative_error (double x, double x_ref)
	Compute the relative error between two values.
double	safe_divide (double numerator, double denominator, double default_value=std::numeric_limits< double >::quiet_NaN())
	Safe division with check for division by zero.
template<typename Iterator >
double	kahan_sum (Iterator first, Iterator last)
	Compute sum with Kahan summation algorithm.
template<typename Iterator , typename Proj >
double	kahan_sum (Iterator first, Iterator last, Proj proj)
	Compute sum with Kahan summation algorithm (with projection)
template<typename Iterator1 , typename Iterator2 >
bool	approx_equal_range (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, double rel_tol=default_rel_tol, double abs_tol=default_abs_tol)
	Check if two ranges are approximately equal element-wise.
template<typename Iterator >
double	interpolate_at (Iterator first, std::size_t n, double p)
	Linear interpolation at position.
template<typename Iterator , typename Projection >
double	interpolate_at (Iterator first, std::size_t n, double p, Projection proj)
	Linear interpolation at position with projection.
template<typename Iterator >
auto	minimum (Iterator first, Iterator last)
	Return minimum value.
template<typename Iterator , typename Projection >
auto	minimum (Iterator first, Iterator last, Projection proj)
	Return minimum value with projection.
template<typename Iterator >
auto	maximum (Iterator first, Iterator last)
	Return maximum value.
template<typename Iterator , typename Projection >
auto	maximum (Iterator first, Iterator last, Projection proj)
	Return maximum value with projection.
template<typename Iterator >
quartile_result	quartiles (Iterator first, Iterator last)
	Return quartiles.
template<typename Iterator , typename Projection >
quartile_result	quartiles (Iterator first, Iterator last, Projection proj)
	Return quartiles with projection.
template<typename Iterator >
double	percentile (Iterator first, Iterator last, double p)
	Return percentile.
template<typename Iterator , typename Projection >
double	percentile (Iterator first, Iterator last, double p, Projection proj)
	Return percentile with projection.
template<typename Iterator >
five_number_summary_result	five_number_summary (Iterator first, Iterator last)
	Return five-number summary.
template<typename Iterator , typename Projection >
five_number_summary_result	five_number_summary (Iterator first, Iterator last, Projection proj)
	Return five-number summary with projection.
template<typename Iterator , typename WeightIterator >
double	weighted_median (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last)
	Weighted median (safe overload)
template<typename Iterator , typename WeightIterator >
double	weighted_median (Iterator first, Iterator last, WeightIterator weight_first)
	Weighted median.
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_median (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, Projection proj)
	Weighted median with projection (safe overload)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_median (Iterator first, Iterator last, WeightIterator weight_first, Projection proj)
	Weighted median with projection.
template<typename Iterator , typename WeightIterator >
double	weighted_percentile (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, double p)
	Weighted percentile (safe overload)
template<typename Iterator , typename WeightIterator >
double	weighted_percentile (Iterator first, Iterator last, WeightIterator weight_first, double p)
	Weighted percentile.
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_percentile (Iterator first, Iterator last, WeightIterator weight_first, WeightIterator weight_last, double p, Projection proj)
	Weighted percentile with projection (safe overload)
template<typename Iterator , typename WeightIterator , typename Projection >
double	weighted_percentile (Iterator first, Iterator last, WeightIterator weight_first, double p, Projection proj)
	Weighted percentile with projection.
template<typename Iterator >
test_result	z_test (Iterator first, Iterator last, double mu0, double sigma, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	One-sample z-test (known variance)
test_result	z_test_proportion (std::size_t successes, std::size_t trials, double p0, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	One-sample proportion z-test.
test_result	z_test_proportion_two_sample (std::size_t successes1, std::size_t trials1, std::size_t successes2, std::size_t trials2, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Two-sample proportion z-test.
template<typename Iterator >
test_result	t_test (Iterator first, Iterator last, double mu0, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	One-sample t-test.
template<typename Iterator1 , typename Iterator2 >
test_result	t_test_two_sample (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Two-sample t-test (independent samples, pooled variance)
template<typename Iterator1 , typename Iterator2 >
test_result	t_test_welch (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Two-sample t-test (Welch's method)
template<typename Iterator1 , typename Iterator2 >
test_result	t_test_paired (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	Paired t-test.
template<typename Iterator1 , typename Iterator2 >
test_result	chisq_test_gof (Iterator1 observed_first, Iterator1 observed_last, Iterator2 expected_first, Iterator2 expected_last)
	Chi-square goodness of fit test.
template<typename Iterator >
test_result	chisq_test_gof_uniform (Iterator observed_first, Iterator observed_last)
	Chi-square goodness of fit test (uniform expected frequencies)
test_result	chisq_test_independence (const std::vector< std::vector< double > > &contingency_table)
	Chi-square test for independence.
template<typename Iterator1 , typename Iterator2 >
test_result	f_test (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, alternative_hypothesis alt=alternative_hypothesis::two_sided)
	F-test (variance comparison)
std::vector< double >	bonferroni_correction (const std::vector< double > &p_values)
	Bonferroni correction.
std::vector< double >	benjamini_hochberg_correction (const std::vector< double > &p_values)
	Benjamini-Hochberg correction (FDR control)
std::vector< double >	holm_correction (const std::vector< double > &p_values)
	Holm correction (step-down Bonferroni method)
double	power_t_test_one_sample (double effect_size, std::size_t n, double alpha=0.05, const std::string &alternative="two.sided")
	Calculate power for one-sample t-test.
std::size_t	sample_size_t_test_one_sample (double effect_size, double power=0.80, double alpha=0.05, const std::string &alternative="two.sided")
	Calculate required sample size for one-sample t-test.
double	power_t_test_two_sample (double effect_size, std::size_t n1, std::size_t n2, double alpha=0.05, const std::string &alternative="two.sided")
	Calculate power for two-sample t-test.
std::size_t	sample_size_t_test_two_sample (double effect_size, double power=0.80, double alpha=0.05, double ratio=1.0, const std::string &alternative="two.sided")
	Calculate required sample size for two-sample t-test (per group)
double	power_prop_test (double p1, double p2, std::size_t n, double alpha=0.05, const std::string &alternative="two.sided")
	Calculate power for two-sample proportion test.
std::size_t	sample_size_prop_test (double p1, double p2, double power=0.80, double alpha=0.05, const std::string &alternative="two.sided")
	Calculate required sample size for two-sample proportion test.
power_result	power_analysis_t_one_sample (double effect_size, std::size_t n, double alpha=0.05, const std::string &alternative="two.sided")
	Power analysis for one-sample t-test (calculate power)
power_result	power_analysis_t_one_sample_n (double effect_size, double power=0.80, double alpha=0.05, const std::string &alternative="two.sided")
	Power analysis for one-sample t-test (calculate sample size)
double	power_t_test_one_sample (double effect_size, std::size_t n, double alpha, alternative_hypothesis alt)
	Calculate power for one-sample t-test (enum overload)
std::size_t	sample_size_t_test_one_sample (double effect_size, double power, double alpha, alternative_hypothesis alt)
	Calculate required sample size for one-sample t-test (enum overload)
double	power_t_test_two_sample (double effect_size, std::size_t n1, std::size_t n2, double alpha, alternative_hypothesis alt)
	Calculate power for two-sample t-test (enum overload)
std::size_t	sample_size_t_test_two_sample (double effect_size, double power, double alpha, double ratio, alternative_hypothesis alt)
	Calculate required sample size for two-sample t-test (enum overload)
double	power_prop_test (double p1, double p2, std::size_t n, double alpha, alternative_hypothesis alt)
	Calculate power for two-sample proportion test (enum overload)
std::size_t	sample_size_prop_test (double p1, double p2, double power, double alpha, alternative_hypothesis alt)
	Calculate required sample size for two-sample proportion test (enum overload)
power_result	power_analysis_t_one_sample (double effect_size, std::size_t n, double alpha, alternative_hypothesis alt)
	Power analysis for one-sample t-test (enum overload, returning struct)
power_result	power_analysis_t_one_sample_n (double effect_size, double power, double alpha, alternative_hypothesis alt)
	Power analysis for one-sample t-test, sample size (enum overload, returning struct)
default_random_engine &	get_random_engine ()
	Singleton accessor for global random engine.
void	set_seed (std::uint64_t seed)
	Set the seed of the random engine.
void	randomize_seed ()
	Randomly reset the random engine seed.
template<typename Iterator , typename Engine = default_random_engine>
std::vector< typename std::iterator_traits< Iterator >::value_type >	bootstrap_sample (Iterator first, Iterator last, Engine &engine)
	Generate a single bootstrap sample.
template<typename Iterator >
std::vector< typename std::iterator_traits< Iterator >::value_type >	bootstrap_sample (Iterator first, Iterator last)
	Generate a single bootstrap sample (using default random engine)
template<typename Iterator , typename Statistic , typename Engine = default_random_engine>
bootstrap_result	bootstrap (Iterator first, Iterator last, Statistic stat_func, std::size_t n_bootstrap=1000, double confidence=0.95, Engine &engine=get_random_engine())
	Perform general bootstrap estimation.
template<typename Iterator , typename Engine = default_random_engine>
bootstrap_result	bootstrap_mean (Iterator first, Iterator last, std::size_t n_bootstrap=1000, double confidence=0.95, Engine &engine=get_random_engine())
	Perform bootstrap estimation of the mean.
template<typename Iterator , typename Engine = default_random_engine>
bootstrap_result	bootstrap_median (Iterator first, Iterator last, std::size_t n_bootstrap=1000, double confidence=0.95, Engine &engine=get_random_engine())
	Perform bootstrap estimation of the median.
template<typename Iterator , typename Engine = default_random_engine>
bootstrap_result	bootstrap_stddev (Iterator first, Iterator last, std::size_t n_bootstrap=1000, double confidence=0.95, Engine &engine=get_random_engine())
	Perform bootstrap estimation of the standard deviation.
template<typename Iterator , typename Statistic , typename Engine = default_random_engine>
bootstrap_result	bootstrap_bca (Iterator first, Iterator last, Statistic stat_func, std::size_t n_bootstrap=1000, double confidence=0.95, Engine &engine=get_random_engine())
	Compute BCa (bias-corrected and accelerated) bootstrap confidence interval.
template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>
permutation_result	permutation_test_two_sample (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, std::size_t n_permutations=10000, Engine &engine=get_random_engine())
	Perform two-sample permutation test (test of difference in means)
template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>
permutation_result	permutation_test_paired (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, std::size_t n_permutations=10000, Engine &engine=get_random_engine())
	Perform paired permutation test.
template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>
permutation_result	permutation_test_correlation (Iterator1 first1, Iterator1 last1, Iterator2 first2, Iterator2 last2, std::size_t n_permutations=10000, Engine &engine=get_random_engine())
	Perform permutation test for correlation.
template<typename Iterator >
double	mad (Iterator first, Iterator last)
	Median Absolute Deviation (MAD)
template<typename Iterator >
double	mad_scaled (Iterator first, Iterator last)
	Scaled MAD for normal distribution.
template<typename Iterator >
outlier_detection_result	detect_outliers_iqr (Iterator first, Iterator last, double k=1.5)
	Outlier detection using IQR method (Tukey's Fences)
template<typename Iterator >
outlier_detection_result	detect_outliers_zscore (Iterator first, Iterator last, double threshold=3.0)
	Outlier detection using Z-score.
template<typename Iterator >
outlier_detection_result	detect_outliers_modified_zscore (Iterator first, Iterator last, double threshold=3.5)
	Outlier detection using Modified Z-score.
template<typename Iterator >
std::vector< double >	winsorize (Iterator first, Iterator last, double limits=0.05)
	Winsorization.
std::vector< double >	cooks_distance (const std::vector< double > &residuals, const std::vector< double > &hat_values, double mse, std::size_t p)
	Calculate Cook's Distance.
std::vector< double >	dffits (const std::vector< double > &residuals, const std::vector< double > &hat_values, double mse)
	Calculate DFFITS.
template<typename Iterator >
double	hodges_lehmann (Iterator first, Iterator last)
	Hodges-Lehmann estimator.
template<typename Iterator >
double	biweight_midvariance (Iterator first, Iterator last, double c=9.0)
	Biweight Midvariance.
template<typename Iterator >
double	population_skewness (Iterator first, Iterator last)
	Calculate population skewness (Fisher's definition)
template<typename Iterator >
double	population_skewness (Iterator first, Iterator last, double precomputed_mean)
	Calculate population skewness with precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	population_skewness (Iterator first, Iterator last, Projection proj)
	Calculate population skewness with projection.
template<typename Iterator , typename Projection >
double	population_skewness (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate population skewness with projection and precomputed mean.
template<typename Iterator >
double	sample_skewness (Iterator first, Iterator last)
	Calculate sample skewness (bias-corrected version)
template<typename Iterator >
double	sample_skewness (Iterator first, Iterator last, double precomputed_mean)
	Calculate sample skewness with precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	sample_skewness (Iterator first, Iterator last, Projection proj)
	Calculate sample skewness with projection.
template<typename Iterator , typename Projection >
double	sample_skewness (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate sample skewness with projection and precomputed mean.
template<typename Iterator >
double	skewness (Iterator first, Iterator last)
	Calculate skewness (alias for sample_skewness)
template<typename Iterator >
double	skewness (Iterator first, Iterator last, double precomputed_mean)
	Calculate skewness (precomputed mean version)
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	skewness (Iterator first, Iterator last, Projection proj)
	Calculate skewness (projection version)
template<typename Iterator , typename Projection >
double	skewness (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate skewness (projection version, precomputed mean)
template<typename Iterator >
double	population_kurtosis (Iterator first, Iterator last)
	Calculate population kurtosis (Excess Kurtosis)
template<typename Iterator >
double	population_kurtosis (Iterator first, Iterator last, double precomputed_mean)
	Calculate population kurtosis with precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	population_kurtosis (Iterator first, Iterator last, Projection proj)
	Calculate population kurtosis with projection.
template<typename Iterator , typename Projection >
double	population_kurtosis (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate population kurtosis with projection and precomputed mean.
template<typename Iterator >
double	sample_kurtosis (Iterator first, Iterator last)
	Calculate sample kurtosis (bias-corrected version)
template<typename Iterator >
double	sample_kurtosis (Iterator first, Iterator last, double precomputed_mean)
	Calculate sample kurtosis with precomputed mean.
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	sample_kurtosis (Iterator first, Iterator last, Projection proj)
	Calculate sample kurtosis with projection.
template<typename Iterator , typename Projection >
double	sample_kurtosis (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate sample kurtosis with projection and precomputed mean.
template<typename Iterator >
double	kurtosis (Iterator first, Iterator last)
	Calculate kurtosis (alias for sample_kurtosis)
template<typename Iterator >
double	kurtosis (Iterator first, Iterator last, double precomputed_mean)
	Calculate kurtosis (precomputed mean version)
template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>
double	kurtosis (Iterator first, Iterator last, Projection proj)
	Calculate kurtosis (projection version)
template<typename Iterator , typename Projection >
double	kurtosis (Iterator first, Iterator last, Projection proj, double precomputed_mean)
	Calculate kurtosis (projection version, precomputed mean)
double	lgamma_impl (double x)
	Internal log-gamma function implementation.
double	lgamma (double x)
	Log-gamma function.
double	tgamma (double x)
	Gamma function.
double	beta (double a, double b)
	Beta function.
double	lbeta (double a, double b)
	Log-beta function.
double	betainc_impl (double a, double b, double x, int recursion_depth)
	Internal regularized incomplete beta function.
double	betainc (double a, double b, double x)
	Regularized incomplete beta function.
double	betaincinv (double a, double b, double p)
	Inverse regularized incomplete beta function.
double	erf (double x)
	Error function.
double	erfc (double x)
	Complementary error function.
double	norm_cdf (double x)
	Standard normal CDF.
double	norm_quantile (double p)
	Standard normal quantile function.
double	gammainc_lower (double a, double x)
	Lower regularized incomplete gamma function.
double	gammainc_upper (double a, double x)
	Upper regularized incomplete gamma function.
double	gammainc_lower_inv (double a, double p)
	Inverse lower regularized incomplete gamma function.
kaplan_meier_result	kaplan_meier (const std::vector< double > &times, const std::vector< bool > &events)
	Estimate Kaplan-Meier survival curve.
logrank_result	logrank_test (const std::vector< double > &times1, const std::vector< bool > &events1, const std::vector< double > &times2, const std::vector< bool > &events2)
	Log-rank test (comparison of two survival curves)
double	median_survival_time (const kaplan_meier_result &km)
	Calculate median survival time.
hazard_rate_result	nelson_aalen (const std::vector< double > &times, const std::vector< bool > &events)
	Nelson-Aalen cumulative hazard estimation.
template<typename Iterator >
double	autocorrelation (Iterator first, Iterator last, std::size_t lag)
	Calculate autocorrelation coefficient (lag k)
template<typename Iterator >
std::vector< double >	acf (Iterator first, Iterator last, std::size_t max_lag)
	Calculate autocorrelation function (ACF) (from lag 0 to max_lag)
template<typename Iterator >
std::vector< double >	pacf (Iterator first, Iterator last, std::size_t max_lag)
	Calculate partial autocorrelation function (PACF) (Durbin-Levinson algorithm)
template<typename Iterator1 , typename Iterator2 >
double	mae (Iterator1 first1, Iterator1 last1, Iterator2 first2)
	Mean Absolute Error (MAE)
template<typename Iterator1 , typename Iterator2 >
double	mse (Iterator1 first1, Iterator1 last1, Iterator2 first2)
	Mean Squared Error (MSE)
template<typename Iterator1 , typename Iterator2 >
double	rmse (Iterator1 first1, Iterator1 last1, Iterator2 first2)
	Root Mean Squared Error (RMSE)
template<typename Iterator1 , typename Iterator2 >
double	mape (Iterator1 first1, Iterator1 last1, Iterator2 first2)
	Mean Absolute Percentage Error (MAPE)
template<typename Iterator >
std::vector< double >	moving_average (Iterator first, Iterator last, std::size_t window)
	Simple moving average.
template<typename Iterator >
std::vector< double >	exponential_moving_average (Iterator first, Iterator last, double alpha)
	Exponential moving average.
template<typename Iterator >
std::vector< double >	diff (Iterator first, Iterator last, std::size_t order=1)
	Difference series (first-order or d-th order differencing)
template<typename Iterator >
std::vector< double >	seasonal_diff (Iterator first, Iterator last, std::size_t period)
	Seasonal differencing.
template<typename Iterator >
std::vector< double >	lag (Iterator first, Iterator last, std::size_t k)
	Generate lag series.

Variables
constexpr double	NA = std::numeric_limits<double>::quiet_NaN()
	Constant representing NA (NaN)
constexpr double	epsilon = std::numeric_limits<double>::epsilon()
	Machine epsilon for double precision.
constexpr double	default_rel_tol = 1e-9
	Default relative tolerance for floating-point comparisons.
constexpr double	default_abs_tol = 1e-12
	Default absolute tolerance for floating-point comparisons.
template<typename T >
constexpr bool	is_random_engine_v = is_random_engine<T>::value
	Variable template version of is_random_engine.
constexpr double	pi = 3.14159265358979323846
	Pi constant.
constexpr double	sqrt_2 = 1.41421356237309504880
	Square root of 2.
constexpr double	sqrt_2_pi = 2.50662827463100050242
	Square root of 2*pi.
constexpr double	log_sqrt_2_pi = 0.91893853320467274178
	Natural logarithm of sqrt(2*pi)

Typedef Documentation

default_random_engine

using statcpp::default_random_engine = typedef std::mt19937_64

Default random engine type (Mersenne Twister 64-bit version)

Definition at line 21 of file random_engine.hpp.

Enumeration Type Documentation

alternative_hypothesis

enum class statcpp::alternative_hypothesis

strong

Enumeration representing the type of alternative hypothesis.

Specifies the direction of the alternative hypothesis in statistical tests.

Enumerator
two_sided	Two-sided test.
less	One-sided test (less than)
greater	One-sided test (greater than)

Definition at line 34 of file parametric_tests.hpp.

distribution_family

enum class statcpp::distribution_family

strong

Distribution family.

Specifies the probability distribution family to use in generalized linear models.

Enumerator
gaussian	Gaussian (normal) distribution.
binomial	Binomial distribution.
poisson	Poisson distribution.
gamma_family	Gamma distribution (gamma_family because gamma is a reserved word)

Definition at line 49 of file glm.hpp.

effect_size_magnitude

enum class statcpp::effect_size_magnitude

strong

Enumeration for effect size magnitude.

Enumerator
negligible	Negligible.
small	Small.
medium	Medium.
large	Large.

Definition at line 426 of file effect_size.hpp.

link_function

enum class statcpp::link_function

strong

Link function types.

Specifies the link function to use in generalized linear models.

Enumerator
identity	Identity link (linear regression)
logit	Logit link (logistic regression)
probit	Probit link.
log	Log link (Poisson regression)
inverse	Inverse link (Gamma regression)
cloglog	Complementary log-log link.

Definition at line 35 of file glm.hpp.

linkage_type

enum class statcpp::linkage_type

strong

Linkage types.

Enumerator
single	Single linkage.
complete	Complete linkage.
average	Average linkage.
ward	Ward's method.

Definition at line 273 of file clustering.hpp.

missing_mechanism

enum class statcpp::missing_mechanism

strong

Missing mechanism types.

Enumeration for classifying the mechanism of missing data.

• MCAR: Missing occurs completely at random
• MAR: Missing depends on observed variables
• MNAR: Missing depends on the missing value itself

Enumerator
mcar	Missing Completely At Random.
mar	Missing At Random.
mnar	Missing Not At Random.
unknown	Cannot be determined.

Definition at line 46 of file missing_data.hpp.

Function Documentation

acf()

template<typename Iterator >

std::vector< double > statcpp::acf	(	Iterator	first,
		Iterator	last,
		std::size_t	max_lag
	)

Calculate autocorrelation function (ACF) (from lag 0 to max_lag)

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
max_lag	Maximum lag

Returns

Vector of autocorrelation coefficients

Exceptions

std::invalid_argument

If range is empty

Definition at line 97 of file time_series.hpp.

adjusted_r_squared()

template<typename IteratorY , typename IteratorPred >

double statcpp::adjusted_r_squared	(	IteratorY	y_first,
		IteratorY	y_last,
		IteratorPred	pred_first,
		IteratorPred	pred_last,
		std::size_t	num_predictors
	)

Calculate adjusted coefficient of determination.

Coefficient of determination adjusted for overfitting due to number of predictors. Adjusted R^2 = 1 - (1 - R^2) * (n - 1) / (n - p - 1)

Template Parameters

IteratorY	Iterator type for observed values
IteratorPred	Iterator type for predicted values

Parameters

y_first	Beginning iterator for observed values
y_last	Ending iterator for observed values
pred_first	Beginning iterator for predicted values
pred_last	Ending iterator for predicted values
num_predictors	Number of predictors (excluding intercept)

Returns

double Adjusted coefficient of determination

Exceptions

std::invalid_argument	If y and predictions have different lengths
std::invalid_argument	If number of observations is not greater than number of predictors + 1

Definition at line 1177 of file linear_regression.hpp.

aic()

double statcpp::aic ( double  log_likelihood, std::size_t  k  )

inline

Calculate AIC (Akaike Information Criterion)

Calculates the Akaike Information Criterion. Smaller values indicate better models.

Parameters

log_likelihood	Log-likelihood
k	Number of parameters

Returns

AIC value

Definition at line 41 of file model_selection.hpp.

aic_linear() [1/2]

double statcpp::aic_linear ( const multiple_regression_result &  model, std::size_t  n  )

inline

Calculate AIC from multiple regression model.

Calculates log-likelihood from multiple regression result and computes AIC.

Parameters

model	Multiple regression result
n	Sample size

Returns

AIC value

Definition at line 76 of file model_selection.hpp.

aic_linear() [2/2]

double statcpp::aic_linear ( const simple_regression_result &  model, std::size_t  n  )

inline

Calculate AIC from simple regression model.

Calculates log-likelihood from simple regression result and computes AIC.

Parameters

model	Simple regression result
n	Sample size

Returns

AIC value

Definition at line 55 of file model_selection.hpp.

aicc()

double statcpp::aicc ( double  log_likelihood, std::size_t  n, std::size_t  k  )

inline

Calculate AICc (corrected AIC)

Calculates the corrected AIC for small samples. Used when sample size is small relative to number of parameters.

Parameters

log_likelihood	Log-likelihood
n	Sample size
k	Number of parameters

Returns

AICc value

Exceptions

std::invalid_argument

If n <= k + 1

Definition at line 99 of file model_selection.hpp.

all_finite()

template<typename Iterator >

bool statcpp::all_finite	(	Iterator	first,
		Iterator	last
	)

Check if all values in a range are finite.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning of sequence
last	End of sequence

Returns

true if all values are finite

Definition at line 102 of file numerical_utils.hpp.

analyze_missing_patterns()

missing_pattern_info statcpp::analyze_missing_patterns ( const std::vector< std::vector< double > > &  data )

inline

Analyze missing patterns.

Analyzes missing patterns in a dataset, calculating missing rate per variable, overall missing rate, and types and frequencies of missing patterns.

Parameters

data	2D data for analysis (rows: observations, columns: variables)

Returns

missing_pattern_info Missing pattern information

Exceptions

std::invalid_argument

If data is empty or row sizes are inconsistent

Definition at line 92 of file missing_data.hpp.

approx_equal()

bool statcpp::approx_equal ( double  a, double  b, double  rel_tol = default_rel_tol, double  abs_tol = default_abs_tol  )

inline

Check if two floating-point numbers are approximately equal.

Uses both relative and absolute tolerance: |a - b| <= max(rel_tol * max(|a|, |b|), abs_tol)

Parameters

a	First value
b	Second value
rel_tol	Relative tolerance (default: 1e-9)
abs_tol	Absolute tolerance (default: 1e-12)

Returns

true if values are approximately equal

Definition at line 43 of file numerical_utils.hpp.

approx_equal_range()

template<typename Iterator1 , typename Iterator2 >

bool statcpp::approx_equal_range	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	rel_tol = default_rel_tol,
		double	abs_tol = default_abs_tol
	)

Check if two ranges are approximately equal element-wise.

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence
rel_tol	Relative tolerance (default: 1e-9)
abs_tol	Absolute tolerance (default: 1e-12)

Returns

true if all corresponding elements are approximately equal

Definition at line 314 of file numerical_utils.hpp.

argmax() [1/2]

template<typename Iterator >

std::size_t statcpp::argmax	(	Iterator	first,
		Iterator	last
	)

Returns the index of the maximum value.

Returns the index of the element with the maximum value in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Index of the maximum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 1149 of file basic_statistics.hpp.

argmax() [2/2]

template<typename Iterator , typename Projection >

std::size_t statcpp::argmax	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Returns the index of the maximum value (projection version)

Returns the index of the element whose projected value is maximum.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Index of the maximum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 1174 of file basic_statistics.hpp.

argmin() [1/2]

template<typename Iterator >

std::size_t statcpp::argmin	(	Iterator	first,
		Iterator	last
	)

Returns the index of the minimum value.

Returns the index of the element with the minimum value in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Index of the minimum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 1097 of file basic_statistics.hpp.

argmin() [2/2]

template<typename Iterator , typename Projection >

std::size_t statcpp::argmin	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Returns the index of the minimum value (projection version)

Returns the index of the element whose projected value is minimum.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Index of the minimum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 1122 of file basic_statistics.hpp.

argsort()

template<typename T >

std::vector< std::size_t > statcpp::argsort	(	const std::vector< T > &	data,
		bool	ascending = true
	)

Return indices in sorted order.

Template Parameters

T

Data type

Parameters

data	Data vector
ascending	true for ascending, false for descending

Returns

Indices in sorted order

Definition at line 598 of file data_wrangling.hpp.

autocorrelation()

template<typename Iterator >

double statcpp::autocorrelation	(	Iterator	first,
		Iterator	last,
		std::size_t	lag
	)

Calculate autocorrelation coefficient (lag k)

Calculates the autocorrelation coefficient at the specified lag for time series data.

Note

About normalization: This implementation normalizes by the variance of all data following Box-Jenkins (1976): rho(k) = gamma(k) / gamma(0) where gamma(k) = (1/n) * sum((x_t - mu)(x_{t+k} - mu)) is the autocovariance.

The denominator always uses gamma(0) (variance of all data), so rho(0) = 1 and |rho(k)| <= 1 is guaranteed for all lags. This is the same method as R's acf() and Python statsmodels.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
lag	Lag (time difference)

Returns

Autocorrelation coefficient [-1, 1]

Exceptions

std::invalid_argument

If range is empty, lag is >= data length, or variance is zero

Definition at line 45 of file time_series.hpp.

bartlett_test()

test_result statcpp::bartlett_test ( const std::vector< std::vector< double > > &  groups )

inline

Perform Bartlett test (homogeneity of variance test)

Tests whether variances are equal across multiple groups. Based on likelihood ratio test assuming normal distribution. For data that may not follow normal distribution, Levene test is recommended.

Parameters

groups

Vector of vectors containing data for each group

Returns

test_result Test result containing chi-square statistic, p-value, and degrees of freedom

Exceptions

std::invalid_argument	If there are fewer than 2 groups
std::invalid_argument	If any group has fewer than 2 elements
std::invalid_argument	If any group has zero or negative variance

Note

Null hypothesis: All groups have equal variance

Sensitive to departures from normality; use levene_test if normality is questionable

Definition at line 482 of file nonparametric_tests.hpp.

benjamini_hochberg_correction()

std::vector< double > statcpp::benjamini_hochberg_correction ( const std::vector< double > &  p_values )

inline

Benjamini-Hochberg correction (FDR control)

Corrects p-values for multiple testing using the Benjamini-Hochberg method. Performs step-up correction to control the false discovery rate (FDR).

Parameters

p_values

Vector of original p-values

Returns

std::vector<double> Vector of corrected p-values

Definition at line 711 of file parametric_tests.hpp.

bernoulli_cdf()

double statcpp::bernoulli_cdf ( std::uint64_t  k, double  p  )

inline

Bernoulli distribution cumulative distribution function (CDF)

Parameters

k	Upper bound
p	Probability of success

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 768 of file discrete_distributions.hpp.

bernoulli_pmf()

double statcpp::bernoulli_pmf ( std::uint64_t  k, double  p  )

inline

Bernoulli distribution probability mass function (PMF)

P(X = k) = p^k * (1-p)^(1-k) for k ∈ {0, 1}

Parameters

k	Outcome (0 or 1)
p	Probability of success

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 746 of file discrete_distributions.hpp.

bernoulli_quantile()

std::uint64_t statcpp::bernoulli_quantile ( double  prob, double  p  )

inline

Bernoulli distribution quantile function.

Parameters

prob	Cumulative probability
p	Probability of success

Returns

Smallest k such that P(X <= k) >= prob

Definition at line 787 of file discrete_distributions.hpp.

bernoulli_rand() [1/2]

std::uint64_t statcpp::bernoulli_rand ( double  p )

inline

Bernoulli distribution random number generation (using default engine)

Parameters

p	Probability of success

Returns

Generated random number (0 or 1)

Definition at line 824 of file discrete_distributions.hpp.

bernoulli_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::bernoulli_rand	(	double	p,
		Engine &	engine
	)

Bernoulli distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

p	Probability of success
engine	Random engine

Returns

Generated random number (0 or 1)

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 809 of file discrete_distributions.hpp.

beta()

double statcpp::beta ( double  a, double  b  )

inline

Beta function.

Computes the beta function B(a, b) = Gamma(a) * Gamma(b) / Gamma(a + b).

Parameters

a	First parameter (must be positive)
b	Second parameter (must be positive)

Returns

B(a, b)

Exceptions

std::domain_error

If a or b is non-positive

Definition at line 148 of file special_functions.hpp.

beta_cdf()

double statcpp::beta_cdf ( double  x, double  alpha, double  beta_param  )

inline

Beta distribution cumulative distribution function (CDF)

F(x) = I_x(alpha, beta) (regularized incomplete beta function)

Parameters

x	Random variable value
alpha	Shape parameter alpha
beta_param	Shape parameter beta

Returns

Cumulative probability

Exceptions

std::invalid_argument

If alpha <= 0 or beta_param <= 0

Definition at line 493 of file continuous_distributions.hpp.

beta_pdf()

double statcpp::beta_pdf ( double  x, double  alpha, double  beta_param  )

inline

Beta distribution probability density function (PDF)

f(x) = x^(alpha-1) * (1-x)^(beta-1) / B(alpha, beta) for 0 < x < 1

Parameters

x	Random variable value
alpha	Shape parameter alpha
beta_param	Shape parameter beta

Returns

Probability density

Exceptions

std::invalid_argument

If alpha <= 0 or beta_param <= 0

Definition at line 459 of file continuous_distributions.hpp.

beta_quantile()

double statcpp::beta_quantile ( double  p, double  alpha, double  beta_param  )

inline

Beta distribution quantile function.

Parameters

p	Probability (0 <= p <= 1)
alpha	Shape parameter alpha
beta_param	Shape parameter beta

Returns

Quantile

Exceptions

std::invalid_argument

If alpha <= 0, beta_param <= 0, or p is outside [0, 1]

Definition at line 516 of file continuous_distributions.hpp.

beta_rand() [1/2]

double statcpp::beta_rand ( double  alpha, double  beta_param  )

inline

Beta distribution random number generation (using default engine)

Parameters

alpha	Shape parameter alpha
beta_param	Shape parameter beta

Returns

Random number following beta distribution

Definition at line 574 of file continuous_distributions.hpp.

beta_rand() [2/2]

template<typename Engine = default_random_engine>

double statcpp::beta_rand	(	double	alpha,
		double	beta_param,
		Engine &	engine
	)

Beta distribution random number generation (using gamma variates)

Template Parameters

Engine

Random engine type

Parameters

alpha	Shape parameter alpha
beta_param	Shape parameter beta
engine	Random engine

Returns

Random number following beta distribution

Exceptions

std::invalid_argument

If alpha <= 0 or beta_param <= 0

Definition at line 544 of file continuous_distributions.hpp.

betainc()

double statcpp::betainc ( double  a, double  b, double  x  )

inline

Regularized incomplete beta function.

Computes the regularized incomplete beta function I_x(a, b).

Parameters

a	First parameter (must be positive)
b	Second parameter (must be positive)
x	Upper limit of integration (must be in [0, 1])

Returns

I_x(a, b)

Exceptions

std::domain_error

If parameters are invalid

Note

Used for computing CDFs of beta, F, and t distributions.

Definition at line 264 of file special_functions.hpp.

betainc_impl()

double statcpp::betainc_impl ( double  a, double  b, double  x, int  recursion_depth  )

inline

Internal regularized incomplete beta function.

Computes the regularized incomplete beta function I_x(a, b) using continued fraction expansion.

Parameters

a	First parameter
b	Second parameter
x	Upper limit of integration (must be in [0, 1])
recursion_depth	Recursion depth for tracking

Returns

I_x(a, b)

Exceptions

std::runtime_error

If recursion depth is exceeded

Note

Reference: Numerical Recipes, Press et al.

Uses Lentz's algorithm

Definition at line 189 of file special_functions.hpp.

betaincinv()

double statcpp::betaincinv ( double  a, double  b, double  p  )

inline

Inverse regularized incomplete beta function.

Computes x such that I_x(a, b) = p (quantile function).

Parameters

a	First parameter (must be positive)
b	Second parameter (must be positive)
p	Probability value (must be in [0, 1])

Returns

x such that I_x(a, b) = p

Exceptions

std::domain_error

If parameters are invalid

Note

Uses Newton-Raphson iteration

Definition at line 291 of file special_functions.hpp.

bic()

double statcpp::bic ( double  log_likelihood, std::size_t  n, std::size_t  k  )

inline

Calculate BIC (Bayesian Information Criterion)

Calculates the Bayesian Information Criterion (Schwarz criterion). Penalizes complex models more heavily than AIC.

Parameters

log_likelihood	Log-likelihood
n	Sample size
k	Number of parameters

Returns

BIC value

Definition at line 122 of file model_selection.hpp.

bic_linear() [1/2]

double statcpp::bic_linear ( const multiple_regression_result &  model, std::size_t  n  )

inline

Calculate BIC from multiple regression model.

Calculates log-likelihood from multiple regression result and computes BIC.

Parameters

model	Multiple regression result
n	Sample size

Returns

BIC value

Definition at line 155 of file model_selection.hpp.

bic_linear() [2/2]

double statcpp::bic_linear ( const simple_regression_result &  model, std::size_t  n  )

inline

Calculate BIC from simple regression model.

Calculates log-likelihood from simple regression result and computes BIC.

Parameters

model	Simple regression result
n	Sample size

Returns

BIC value

Definition at line 136 of file model_selection.hpp.

bin_equal_freq()

std::vector< std::size_t > statcpp::bin_equal_freq ( const std::vector< double > &  data, std::size_t  n_bins  )

inline

Binning (equal frequency)

Parameters

data	Data vector
n_bins	Number of bins

Returns

Vector of bin numbers

Definition at line 1058 of file data_wrangling.hpp.

bin_equal_width()

std::vector< std::size_t > statcpp::bin_equal_width ( const std::vector< double > &  data, std::size_t  n_bins  )

inline

Binning (equal width)

Parameters

data	Data vector
n_bins	Number of bins

Returns

Vector of bin numbers

Definition at line 1021 of file data_wrangling.hpp.

binomial_cdf()

double statcpp::binomial_cdf ( std::uint64_t  k, std::uint64_t  n, double  p  )

inline

Binomial distribution cumulative distribution function (CDF)

Calculates P(X <= k).

Parameters

k	Upper bound of number of successes
n	Number of trials
p	Probability of success in each trial

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 111 of file discrete_distributions.hpp.

binomial_coef()

double statcpp::binomial_coef ( std::uint64_t  n, std::uint64_t  k  )

inline

Calculate binomial coefficient.

Calculates C(n, k) = n! / (k! * (n-k)!)

Parameters

n	Total number of elements
k	Number of elements to choose

Returns

Value of C(n, k)

Definition at line 65 of file discrete_distributions.hpp.

binomial_pmf()

double statcpp::binomial_pmf ( std::uint64_t  k, std::uint64_t  n, double  p  )

inline

Binomial distribution probability mass function (PMF)

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Parameters

k	Number of successes
n	Number of trials
p	Probability of success in each trial

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 86 of file discrete_distributions.hpp.

binomial_quantile()

std::uint64_t statcpp::binomial_quantile ( double  prob, std::uint64_t  n, double  p  )

inline

Binomial distribution quantile function.

Returns the smallest k such that P(X <= k) >= prob.

Parameters

prob	Probability value
n	Number of trials
p	Probability of success in each trial

Returns

Quantile

Exceptions

std::invalid_argument

If prob or p is in an invalid range

Definition at line 134 of file discrete_distributions.hpp.

binomial_rand() [1/2]

std::uint64_t statcpp::binomial_rand ( std::uint64_t  n, double  p  )

inline

Binomial distribution random number generation (using default engine)

Parameters

n	Number of trials
p	Probability of success in each trial

Returns

Generated random number

Definition at line 188 of file discrete_distributions.hpp.

binomial_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::binomial_rand	(	std::uint64_t	n,
		double	p,
		Engine &	engine
	)

Binomial distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

n	Number of trials
p	Probability of success in each trial
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If p is outside [0, 1]

Definition at line 172 of file discrete_distributions.hpp.

biweight_midvariance()

template<typename Iterator >

double statcpp::biweight_midvariance	(	Iterator	first,
		Iterator	last,
		double	c = 9.0
	)

Biweight Midvariance.

Calculates the Biweight Midvariance, a robust variance estimator.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range
c	Tuning constant (default: 9.0)

Returns

Biweight midvariance

Exceptions

std::invalid_argument

If range has less than 2 elements

Note

A variance estimator less affected by outliers.

Definition at line 517 of file robust.hpp.

bonferroni_correction()

std::vector< double > statcpp::bonferroni_correction ( const std::vector< double > &  p_values )

inline

Bonferroni correction.

Corrects p-values for multiple testing using the Bonferroni method. Each p-value is multiplied by the number of tests, capped at 1.

Parameters

p_values

Vector of original p-values

Returns

std::vector<double> Vector of corrected p-values

Definition at line 690 of file parametric_tests.hpp.

bonferroni_posthoc()

posthoc_result statcpp::bonferroni_posthoc ( const one_way_anova_result &  anova_result, double  alpha = 0.05  )

inline

Perform Bonferroni method for multiple comparisons.

Performs multiple comparisons among all pairs of groups with Bonferroni correction as a post-hoc test following one-way ANOVA.

Parameters

anova_result	Result from one-way ANOVA
alpha	Significance level (default: 0.05)

Returns

posthoc_result Post-hoc comparison results

Exceptions

std::invalid_argument

If alpha is outside the range (0, 1)

Definition at line 444 of file anova.hpp.

bootstrap()

template<typename Iterator , typename Statistic , typename Engine = default_random_engine>

bootstrap_result statcpp::bootstrap	(	Iterator	first,
		Iterator	last,
		Statistic	stat_func,
		std::size_t	n_bootstrap = 1000,
		double	confidence = 0.95,
		Engine &	engine = get_random_engine()
	)

Perform general bootstrap estimation.

Applies the bootstrap method to any statistical function and computes the estimated statistic, standard error, percentile confidence interval, and bias.

Percentile confidence interval calculation:

• Lower index: floor(alpha/2 * B)
• Upper index: floor((1 - alpha/2) * B) - 1
• Where alpha = 1 - confidence, B = n_bootstrap

Note

The percentile method is the simplest confidence interval calculation method. For more accurate confidence intervals, use bootstrap_bca().

Template Parameters

Iterator	Input iterator type
Statistic	Statistical function type (function taking iterator pair and returning double)
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
stat_func	Function object that computes the statistic
n_bootstrap	Number of bootstrap iterations (default: 1000)
confidence	Confidence level (default: 0.95)
engine	Reference to random engine

Returns

bootstrap_result structure containing bootstrap estimation results

Exceptions

std::invalid_argument	If confidence is outside (0, 1)
std::invalid_argument	If number of input elements is less than 2

Definition at line 139 of file resampling.hpp.

bootstrap_bca()

template<typename Iterator , typename Statistic , typename Engine = default_random_engine>

bootstrap_result statcpp::bootstrap_bca	(	Iterator	first,
		Iterator	last,
		Statistic	stat_func,
		std::size_t	n_bootstrap = 1000,
		double	confidence = 0.95,
		Engine &	engine = get_random_engine()
	)

Compute BCa (bias-corrected and accelerated) bootstrap confidence interval.

Implements the BCa method which provides more accurate confidence intervals than the standard percentile method. Uses jackknife to estimate the acceleration factor and applies bias correction.

Template Parameters

Iterator	Input iterator type
Statistic	Statistical function type (function taking iterator pair and returning double)
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
stat_func	Function object that computes the statistic
n_bootstrap	Number of bootstrap iterations (default: 1000)
confidence	Confidence level (default: 0.95)
engine	Reference to random engine

Returns

bootstrap_result structure containing bootstrap estimation results

Exceptions

std::invalid_argument	If confidence is outside (0, 1)
std::invalid_argument	If number of input elements is less than 3

Definition at line 310 of file resampling.hpp.

bootstrap_mean()

template<typename Iterator , typename Engine = default_random_engine>

bootstrap_result statcpp::bootstrap_mean	(	Iterator	first,
		Iterator	last,
		std::size_t	n_bootstrap = 1000,
		double	confidence = 0.95,
		Engine &	engine = get_random_engine()
	)

Perform bootstrap estimation of the mean.

Applies the bootstrap method to the sample mean and computes standard error and confidence interval.

Template Parameters

Iterator	Input iterator type
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
n_bootstrap	Number of bootstrap iterations (default: 1000)
confidence	Confidence level (default: 0.95)
engine	Reference to random engine

Returns

bootstrap_result structure containing bootstrap estimation results

Exceptions

std::invalid_argument	If confidence is outside (0, 1)
std::invalid_argument	If number of input elements is less than 2

Definition at line 221 of file resampling.hpp.

bootstrap_median()

template<typename Iterator , typename Engine = default_random_engine>

bootstrap_result statcpp::bootstrap_median	(	Iterator	first,
		Iterator	last,
		std::size_t	n_bootstrap = 1000,
		double	confidence = 0.95,
		Engine &	engine = get_random_engine()
	)

Perform bootstrap estimation of the median.

Applies the bootstrap method to the sample median and computes standard error and confidence interval.

Template Parameters

Iterator	Input iterator type
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
n_bootstrap	Number of bootstrap iterations (default: 1000)
confidence	Confidence level (default: 0.95)
engine	Reference to random engine

Returns

bootstrap_result structure containing bootstrap estimation results

Exceptions

std::invalid_argument	If confidence is outside (0, 1)
std::invalid_argument	If number of input elements is less than 2

Definition at line 247 of file resampling.hpp.

bootstrap_sample() [1/2]

template<typename Iterator >

std::vector< typename std::iterator_traits< Iterator >::value_type > statcpp::bootstrap_sample	(	Iterator	first,
		Iterator	last
	)

Generate a single bootstrap sample (using default random engine)

Generates a bootstrap sample using the global default random engine.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of input range
last	End iterator of input range

Returns

Bootstrap sample obtained by sampling with replacement

Exceptions

std::invalid_argument

If input range is empty

Definition at line 102 of file resampling.hpp.

bootstrap_sample() [2/2]

template<typename Iterator , typename Engine = default_random_engine>

std::vector< typename std::iterator_traits< Iterator >::value_type > statcpp::bootstrap_sample	(	Iterator	first,
		Iterator	last,
		Engine &	engine
	)

Generate a single bootstrap sample.

Generates a bootstrap sample of the same size as the original sample by sampling with replacement from the given data.

Template Parameters

Iterator	Input iterator type
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
engine	Reference to random engine

Returns

Bootstrap sample obtained by sampling with replacement

Exceptions

std::invalid_argument

If input range is empty

Definition at line 69 of file resampling.hpp.

bootstrap_stddev()

template<typename Iterator , typename Engine = default_random_engine>

bootstrap_result statcpp::bootstrap_stddev	(	Iterator	first,
		Iterator	last,
		std::size_t	n_bootstrap = 1000,
		double	confidence = 0.95,
		Engine &	engine = get_random_engine()
	)

Perform bootstrap estimation of the standard deviation.

Applies the bootstrap method to the sample standard deviation and computes standard error and confidence interval.

Template Parameters

Iterator	Input iterator type
Engine	Random engine type (default: default_random_engine)

Parameters

first	Beginning iterator of input range
last	End iterator of input range
n_bootstrap	Number of bootstrap iterations (default: 1000)
confidence	Confidence level (default: 0.95)
engine	Reference to random engine

Returns

bootstrap_result structure containing bootstrap estimation results

Exceptions

std::invalid_argument	If confidence is outside (0, 1)
std::invalid_argument	If number of input elements is less than 2

Definition at line 277 of file resampling.hpp.

boxcox_transform()

std::vector< double > statcpp::boxcox_transform ( const std::vector< double > &  data, double  lambda  )

inline

Box-Cox transformation.

When lambda = 0, performs logarithmic transformation

Parameters

data	Data vector
lambda	Transformation parameter

Returns

Box-Cox transformed data (values <= 0 become NA)

Definition at line 390 of file data_wrangling.hpp.

chebyshev_distance() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::chebyshev_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Chebyshev distance (L∞ norm, maximum metric)

Computes the maximum absolute difference: d(x, y) = max(|x_i - y_i|)

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence

Returns

Chebyshev distance

Exceptions

std::invalid_argument

if sequences have different lengths

Definition at line 487 of file distance_metrics.hpp.

chebyshev_distance() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::chebyshev_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Proj1	proj1,
		Proj2	proj2
	)

Chebyshev distance with projection.

Definition at line 520 of file distance_metrics.hpp.

chisq_cdf()

double statcpp::chisq_cdf ( double  x, double  df  )

inline

Chi-square distribution cumulative distribution function (CDF)

Chi-square distribution is a special case of gamma distribution: chi^2(df) = Gamma(df/2, 1/2) This implementation uses the regularized incomplete gamma function: F(x; df) = gamma(df/2, x/2) / Gamma(df/2) = P(df/2, x/2)

Parameters

x	Random variable value
df	Degrees of freedom

Returns

Cumulative probability

Exceptions

std::invalid_argument

If df <= 0

Definition at line 613 of file continuous_distributions.hpp.

chisq_pdf()

double statcpp::chisq_pdf ( double  x, double  df  )

inline

Chi-square distribution probability density function (PDF)

Special case of gamma distribution (shape = df/2, rate = 1/2)

Parameters

x	Random variable value
df	Degrees of freedom

Returns

Probability density

Exceptions

std::invalid_argument

If df <= 0

Definition at line 593 of file continuous_distributions.hpp.

chisq_quantile()

double statcpp::chisq_quantile ( double  p, double  df  )

inline

Chi-square distribution quantile function.

Parameters

p	Probability (0 <= p <= 1)
df	Degrees of freedom

Returns

Quantile

Exceptions

std::invalid_argument

If df <= 0 or p is outside [0, 1]

Definition at line 629 of file continuous_distributions.hpp.

chisq_rand() [1/2]

double statcpp::chisq_rand ( double  df )

inline

Chi-square distribution random number generation (using default engine)

Parameters

df	Degrees of freedom

Returns

Random number following chi-square distribution

Definition at line 661 of file continuous_distributions.hpp.

chisq_rand() [2/2]

template<typename Engine = default_random_engine>

double statcpp::chisq_rand	(	double	df,
		Engine &	engine
	)

Chi-square distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

df	Degrees of freedom
engine	Random engine

Returns

Random number following chi-square distribution

Exceptions

std::invalid_argument

If df <= 0

Definition at line 647 of file continuous_distributions.hpp.

chisq_test_gof()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::chisq_test_gof	(	Iterator1	observed_first,
		Iterator1	observed_last,
		Iterator2	expected_first,
		Iterator2	expected_last
	)

Chi-square goodness of fit test.

Tests whether observed frequencies match expected frequencies.

Template Parameters

Iterator1	Input iterator type for observed frequencies
Iterator2	Input iterator type for expected frequencies

Parameters

observed_first	Beginning iterator of observed frequencies
observed_last	End iterator of observed frequencies
expected_first	Beginning iterator of expected frequencies
expected_last	End iterator of expected frequencies

Returns

test_result Test result (chi-square statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If observed and expected lengths differ, fewer than 2 categories, or expected frequency is non-positive

Definition at line 464 of file parametric_tests.hpp.

chisq_test_gof_uniform()

template<typename Iterator >

test_result statcpp::chisq_test_gof_uniform	(	Iterator	observed_first,
		Iterator	observed_last
	)

Chi-square goodness of fit test (uniform expected frequencies)

Tests whether observed frequencies follow a uniform distribution.

Template Parameters

Iterator

Input iterator type for observed frequencies

Parameters

observed_first	Beginning iterator of observed frequencies
observed_last	End iterator of observed frequencies

Returns

test_result Test result (chi-square statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If fewer than 2 categories

Definition at line 513 of file parametric_tests.hpp.

chisq_test_independence()

test_result statcpp::chisq_test_independence ( const std::vector< std::vector< double > > &  contingency_table )

inline

Chi-square test for independence.

Tests independence of two variables based on a contingency table.

Parameters

contingency_table

Contingency table (2D array in row-major order)

Returns

test_result Test result (chi-square statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If rows or columns are less than 2, column counts are inconsistent, negative values exist, or table is empty

Definition at line 556 of file parametric_tests.hpp.

ci_mean() [1/2]

template<typename Iterator , typename Projection >

confidence_interval statcpp::ci_mean	(	Iterator	first,
		Iterator	last,
		double	confidence,
		Projection	proj
	)

Calculate confidence interval for mean (projection version)

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
confidence	Confidence level
proj	Projection function

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or there are fewer than 2 elements

Definition at line 155 of file estimation.hpp.

ci_mean() [2/2]

template<typename Iterator >

confidence_interval statcpp::ci_mean	(	Iterator	first,
		Iterator	last,
		double	confidence = 0.95
	)

Calculate confidence interval for mean (t-distribution based)

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or there are fewer than 2 elements

Definition at line 119 of file estimation.hpp.

ci_mean_diff()

template<typename Iterator1 , typename Iterator2 >

confidence_interval statcpp::ci_mean_diff	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	confidence = 0.95
	)

Calculate confidence interval for difference of two-sample means (independent samples, pooled variance)

Calculates the confidence interval for the difference of two-sample means assuming equal variances.

Template Parameters

Iterator1	First iterator type
Iterator2	Second iterator type

Parameters

first1	Beginning iterator of first data range
last1	Ending iterator of first data range
first2	Beginning iterator of second data range
last2	Ending iterator of second data range
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or either sample has fewer than 2 elements

Definition at line 354 of file estimation.hpp.

ci_mean_diff_pooled()

template<typename Iterator1 , typename Iterator2 >

confidence_interval statcpp::ci_mean_diff_pooled	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	confidence = 0.95
	)

Calculate confidence interval for two-sample mean difference (assuming equal variances)

Template Parameters

Iterator1	First iterator type
Iterator2	Second iterator type

Parameters

first1	Beginning iterator of first data range
last1	Ending iterator of first data range
first2	Beginning iterator of second data range
last2	Ending iterator of second data range
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or either sample has fewer than 2 elements

Definition at line 669 of file estimation.hpp.

ci_mean_diff_welch()

template<typename Iterator1 , typename Iterator2 >

confidence_interval statcpp::ci_mean_diff_welch	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	confidence = 0.95
	)

Calculate confidence interval for difference of two-sample means (Welch method, not assuming equal variances)

Calculates the confidence interval for the difference of two-sample means without assuming equal variances (Welch-Satterthwaite method).

Template Parameters

Iterator1	First iterator type
Iterator2	Second iterator type

Parameters

first1	Beginning iterator of first data range
last1	Ending iterator of first data range
first2	Beginning iterator of second data range
last2	Ending iterator of second data range
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1), either sample has fewer than 2 elements, or both variances are zero

Definition at line 405 of file estimation.hpp.

ci_mean_z()

template<typename Iterator >

confidence_interval statcpp::ci_mean_z	(	Iterator	first,
		Iterator	last,
		double	sigma,
		double	confidence = 0.95
	)

Calculate confidence interval for mean (z-distribution based, known variance)

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
sigma	Known population standard deviation
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1), sigma is not positive, or the range is empty

Definition at line 194 of file estimation.hpp.

ci_proportion()

confidence_interval statcpp::ci_proportion ( std::size_t  successes, std::size_t  trials, double  confidence = 0.95  )

inline

Calculate confidence interval for proportion (Wald method)

Parameters

successes	Number of successes
trials	Number of trials
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1), trials is 0, or successes exceeds trials

Definition at line 232 of file estimation.hpp.

ci_proportion_diff()

confidence_interval statcpp::ci_proportion_diff ( std::size_t  successes1, std::size_t  n1, std::size_t  successes2, std::size_t  n2, double  confidence = 0.95  )

inline

Calculate confidence interval for two-sample proportion difference.

Parameters

successes1	Number of successes in first sample
n1	First sample size
successes2	Number of successes in second sample
n2	Second sample size
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 692 of file estimation.hpp.

ci_proportion_wilson()

confidence_interval statcpp::ci_proportion_wilson ( std::size_t  successes, std::size_t  trials, double  confidence = 0.95  )

inline

Calculate confidence interval for proportion (Wilson method, recommended)

The Wilson method has better properties than the Wald method, especially for small samples or extreme proportions.

Parameters

successes	Number of successes
trials	Number of trials
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1), trials is 0, or successes exceeds trials

Definition at line 269 of file estimation.hpp.

ci_variance()

template<typename Iterator >

confidence_interval statcpp::ci_variance	(	Iterator	first,
		Iterator	last,
		double	confidence = 0.95
	)

Calculate confidence interval for variance (chi-square distribution based)

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
confidence	Confidence level (default: 0.95)

Returns

Confidence interval

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or there are fewer than 2 elements

Definition at line 310 of file estimation.hpp.

clamp()

double statcpp::clamp ( double  x, double  min_val, double  max_val  )

inline

Clamp a value to a range [min_val, max_val].

Parameters

x	Value to clamp
min_val	Minimum value
max_val	Maximum value

Returns

Clamped value

Exceptions

std::invalid_argument

if min_val > max_val

Definition at line 199 of file numerical_utils.hpp.

coefficient_of_variation() [1/4]

template<typename Iterator >

double statcpp::coefficient_of_variation	(	Iterator	first,
		Iterator	last
	)

Coefficient of variation.

Computes the standard deviation divided by the mean (returned as a ratio; multiply by 100 for percentage). Useful for measuring relative variability of data.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Coefficient of variation (ratio)

Exceptions

std::invalid_argument

If range is empty, has fewer than 2 elements, or mean is zero

Definition at line 832 of file dispersion_spread.hpp.

coefficient_of_variation() [2/4]

template<typename Iterator >

double statcpp::coefficient_of_variation	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Coefficient of variation using precomputed mean.

Computes coefficient of variation when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Coefficient of variation (ratio)

Exceptions

std::invalid_argument

If range is empty, has fewer than 2 elements, or mean is zero

Definition at line 861 of file dispersion_spread.hpp.

coefficient_of_variation() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::coefficient_of_variation	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Coefficient of variation of projected values using a lambda expression.

Computes the coefficient of variation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Coefficient of variation of projected values (ratio)

Exceptions

std::invalid_argument

If range is empty, has fewer than 2 elements, or mean is zero

Definition at line 893 of file dispersion_spread.hpp.

coefficient_of_variation() [4/4]

template<typename Iterator , typename Projection >

double statcpp::coefficient_of_variation	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Coefficient of variation of projected values using precomputed mean.

Computes coefficient of variation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Coefficient of variation of projected values (ratio)

Exceptions

std::invalid_argument

If range is empty, has fewer than 2 elements, or mean is zero

Definition at line 924 of file dispersion_spread.hpp.

cohens_d() [1/2]

template<typename Iterator >

double statcpp::cohens_d	(	Iterator	first,
		Iterator	last,
		double	mu0
	)

Cohen's d (one-sample, using sample standard deviation)

Calculates the standardized mean difference using the sample standard deviation.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	Ending iterator
mu0	Population mean to compare against

Returns

Cohen's d

Exceptions

std::invalid_argument

If there are fewer than 2 elements or variance is zero

Definition at line 63 of file effect_size.hpp.

cohens_d() [2/2]

template<typename Iterator >

double statcpp::cohens_d	(	Iterator	first,
		Iterator	last,
		double	mu0,
		double	sigma
	)

Cohen's d (one-sample, known population standard deviation)

Calculates the standardized mean difference. Used when the population standard deviation is known.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	Ending iterator
mu0	Population mean to compare against
sigma	Population standard deviation

Returns

Cohen's d

Exceptions

std::invalid_argument

If the range is empty or sigma is not positive

Definition at line 35 of file effect_size.hpp.

cohens_d_two_sample()

template<typename Iterator1 , typename Iterator2 >

double statcpp::cohens_d_two_sample	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Cohen's d (two-sample, pooled standard deviation)

Calculates the standardized mean difference between two groups. Uses pooled standard deviation.

Template Parameters

Iterator1	RandomAccessIterator type for first sample
Iterator2	RandomAccessIterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	Ending iterator of first sample
first2	Beginning iterator of second sample
last2	Ending iterator of second sample

Returns

Cohen's d

Exceptions

std::invalid_argument

If either sample has fewer than 2 elements or pooled variance is zero

Definition at line 96 of file effect_size.hpp.

cohens_f()

double statcpp::cohens_f ( const one_way_anova_result &  result )

inline

Calculate Cohen's f for one-way ANOVA.

Standardized effect size measure where 0.10 indicates small, 0.25 indicates medium, and 0.40 indicates large effect.

Parameters

result

Result from one-way ANOVA

Returns

double Cohen's f value (infinity if eta_squared equals 1.0)

Definition at line 922 of file anova.hpp.

cohens_h()

double statcpp::cohens_h ( double  p1, double  p2  )

inline

Cohen's h (effect size for difference between two proportions)

Calculates the effect size representing the difference between two proportions.

Parameters

p1	Proportion in first group
p2	Proportion in second group

Returns

Cohen's h

Exceptions

std::invalid_argument

If proportions are outside [0, 1] range

Definition at line 355 of file effect_size.hpp.

compute_glm_residuals()

glm_residuals statcpp::compute_glm_residuals ( const glm_result &  model, const std::vector< std::vector< double > > &  X, const std::vector< double > &  y  )

inline

Calculate GLM residuals.

Calculates various types of residuals from a fitted GLM model.

Parameters

model	Fitted GLM model
X	Predictor matrix
y	Response variable vector

Returns

Structure containing various residuals

Exceptions

std::invalid_argument

If X and Y sizes don't match

Definition at line 890 of file glm.hpp.

compute_ranks_with_ties()

template<typename Iterator >

std::vector< double > statcpp::compute_ranks_with_ties	(	Iterator	first,
		Iterator	last
	)

Compute ranks with tie handling.

Assigns ranks to input data. Elements with the same value are assigned average ranks.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of range
last	Ending iterator of range

Returns

std::vector<double> Vector of ranks corresponding to each element

Note

Returns an empty vector if an empty range is passed.

Definition at line 56 of file nonparametric_tests.hpp.

compute_residual_diagnostics() [1/2]

residual_diagnostics statcpp::compute_residual_diagnostics ( const multiple_regression_result &  model, const std::vector< std::vector< double > > &  X, const std::vector< double > &  y  )

inline

Perform residual diagnostics for multiple regression model.

Calculates residuals, standardized residuals, studentized residuals, leverage values, Cook's distance, and Durbin-Watson statistic.

Parameters

model	Multiple regression analysis results
X	Predictor matrix
y	Response variable vector

Returns

residual_diagnostics Residual diagnostics results

Exceptions

std::invalid_argument

If X and y have different lengths

Definition at line 879 of file linear_regression.hpp.

compute_residual_diagnostics() [2/2]

template<typename IteratorX , typename IteratorY >

residual_diagnostics statcpp::compute_residual_diagnostics	(	const simple_regression_result &	model,
		IteratorX	x_first,
		IteratorX	x_last,
		IteratorY	y_first,
		IteratorY	y_last
	)

Perform residual diagnostics for simple regression model.

Calculates residuals, standardized residuals, studentized residuals, leverage values, Cook's distance, and Durbin-Watson statistic.

Template Parameters

IteratorX	Iterator type for predictor variable
IteratorY	Iterator type for response variable

Parameters

model	Simple regression analysis results
x_first	Beginning iterator for predictor variable
x_last	Ending iterator for predictor variable
y_first	Beginning iterator for response variable
y_last	Ending iterator for response variable

Returns

residual_diagnostics Residual diagnostics results

Exceptions

std::invalid_argument

If x and y have different lengths

Definition at line 798 of file linear_regression.hpp.

compute_tie_groups()

std::vector< std::size_t > statcpp::compute_tie_groups ( const std::vector< double > &  sorted_values )

inline

Compute tie group sizes from sorted data.

Returns a vector of tie group sizes t_j, where each t_j > 1 represents a group of tied values. Used for tie corrections in nonparametric tests.

Parameters

sorted_values

Sorted vector of values

Returns

std::vector<std::size_t> Vector of tie group sizes (only groups with t > 1)

Definition at line 101 of file nonparametric_tests.hpp.

compute_vif()

std::vector< double > statcpp::compute_vif ( const std::vector< std::vector< double > > &  X )

inline

Calculate VIF (Variance Inflation Factor) for each predictor.

VIF is an indicator of multicollinearity, showing the degree to which each predictor is explained by other predictors. Generally VIF > 10 suggests a multicollinearity problem.

Parameters

X	Predictor matrix (n x p)

Returns

std::vector<double> VIF for each predictor

Exceptions

std::invalid_argument	If there are fewer than 3 observations
std::invalid_argument	If there are fewer than 2 predictors

Definition at line 976 of file linear_regression.hpp.

confidence_interval_mean()

template<typename IteratorX >

prediction_interval statcpp::confidence_interval_mean	(	const simple_regression_result &	model,
		IteratorX	x_first,
		IteratorX	x_last,
		double	x_new,
		double	confidence = 0.95
	)

Calculate confidence interval for mean of simple regression model.

Calculates the confidence interval for the mean response at a specific x value. The confidence interval shows the probability that the true regression line is within this interval.

Template Parameters

IteratorX

Iterator type for predictor variable

Parameters

model	Simple regression analysis results
x_first	Beginning iterator for original predictor variable data
x_last	Ending iterator for original predictor variable data
x_new	x value of the point to predict
confidence	Confidence level (default: 0.95)

Returns

prediction_interval Predicted value and confidence interval

Exceptions

std::invalid_argument

If confidence is outside (0, 1) range

Definition at line 744 of file linear_regression.hpp.

contingency_table()

contingency_table_result statcpp::contingency_table ( const std::vector< std::size_t > &  row_data, const std::vector< std::size_t > &  col_data  )

inline

Create a contingency table.

Creates a contingency table (cross-tabulation) from two categorical variables.

Parameters

row_data	Row category values (integers starting from 0)
col_data	Column category values (integers starting from 0)

Returns

Contingency table result

Exceptions

std::invalid_argument

If data lengths do not match or if data is empty

Definition at line 42 of file categorical.hpp.

cooks_distance()

std::vector< double > statcpp::cooks_distance ( const std::vector< double > &  residuals, const std::vector< double > &  hat_values, double  mse, std::size_t  p  )

inline

Calculate Cook's Distance.

Calculates Cook's Distance to detect influential observations in linear regression.

Parameters

residuals	Residuals
hat_values	Leverage values (hat values)
mse	Mean squared error
p	Number of parameters (including intercept)

Returns

Cook's distances

Exceptions

std::invalid_argument

If parameters are invalid

Note

D_i > 1 indicates the observation is influential.

D_i > 4/n is also sometimes used as a threshold.

Definition at line 363 of file robust.hpp.

correlation_matrix()

std::vector< std::vector< double > > statcpp::correlation_matrix ( const std::vector< std::vector< double > > &  data )

inline

Calculate Pearson correlation matrix.

Calculates the correlation matrix for multivariate data. Standardizes the covariance matrix to obtain correlation coefficients.

Parameters

data	Matrix data (rows=observations, columns=variables)

Returns

Correlation matrix (p x p)

Exceptions

std::invalid_argument

If data is empty, rows have different column counts, there are fewer than 2 observations, or any variable has zero variance

Definition at line 89 of file multivariate.hpp.

correlation_matrix_determinant()

double statcpp::correlation_matrix_determinant ( const std::vector< std::vector< double > > &  X )

inline

Calculate determinant of correlation matrix.

Used for multicollinearity diagnostics. det(R) close to 0 indicates strong multicollinearity, det(R) = 1 indicates no correlation between variables.

Parameters

X	Predictor matrix (n x p)

Returns

double Determinant of correlation matrix

Exceptions

std::invalid_argument	If there are fewer than 2 observations
std::invalid_argument	If there are fewer than 2 or more than 3 predictors (only 2 or 3 supported)

Definition at line 1035 of file linear_regression.hpp.

correlation_matrix_pairwise()

std::vector< std::vector< double > > statcpp::correlation_matrix_pairwise ( const std::vector< std::vector< double > > &  data )

inline

Correlation matrix using available case analysis (pairwise deletion)

Calculates correlation coefficients using only cases where both variables are observed for each pair of variables. Also called pairwise deletion.

Parameters

data	Input data (rows: observations, columns: variables)

Returns

std::vector<std::vector<double>> Correlation matrix (NA if insufficient observations)

Definition at line 1100 of file missing_data.hpp.

cosine_distance() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::cosine_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Cosine distance.

Defined as: distance = 1 - similarity Returns a value in [0, 2], where 0 means identical direction

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence

Returns

Cosine distance

Definition at line 288 of file distance_metrics.hpp.

cosine_distance() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::cosine_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Proj1	proj1,
		Proj2	proj2
	)

Cosine distance with projection.

Definition at line 298 of file distance_metrics.hpp.

cosine_similarity() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::cosine_similarity	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Cosine similarity.

Computes the cosine of the angle between two vectors: similarity(x, y) = (x · y) / (||x|| * ||y||)

Returns a value in [-1, 1]:

• 1: vectors point in the same direction
• 0: vectors are orthogonal
• -1: vectors point in opposite directions

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence

Returns

Cosine similarity

Exceptions

std::invalid_argument

if sequences have different lengths or if either vector has zero norm

Definition at line 190 of file distance_metrics.hpp.

cosine_similarity() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::cosine_similarity	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Proj1	proj1,
		Proj2	proj2
	)

Cosine similarity with projection.

Definition at line 233 of file distance_metrics.hpp.

count()

template<typename Iterator >

std::size_t statcpp::count	(	Iterator	first,
		Iterator	last
	)

Data count.

Returns the number of elements in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Number of elements

Definition at line 91 of file basic_statistics.hpp.

covariance() [1/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Covariance (alias for sample_covariance)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Sample covariance

Definition at line 303 of file correlation_covariance.hpp.

covariance() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	mean_x,
		double	mean_y
	)

Covariance with precomputed means (alias for sample_covariance)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
mean_x	Mean of the first data
mean_y	Mean of the second data

Returns

Sample covariance

Definition at line 323 of file correlation_covariance.hpp.

covariance() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Covariance (projection version, alias for sample_covariance)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Sample covariance

Definition at line 346 of file correlation_covariance.hpp.

covariance_matrix()

std::vector< std::vector< double > > statcpp::covariance_matrix ( const std::vector< std::vector< double > > &  data )

inline

Calculate sample covariance matrix.

Calculates the covariance matrix for multivariate data. Data is passed with rows=observations and columns=variables.

Parameters

data	Matrix data (rows=observations, columns=variables)

Returns

Covariance matrix (p x p)

Exceptions

std::invalid_argument

If data is empty, rows have different column counts, or there are fewer than 2 observations

Definition at line 37 of file multivariate.hpp.

create_cv_folds()

std::vector< std::vector< std::size_t > > statcpp::create_cv_folds ( std::size_t  n, std::size_t  k, bool  shuffle = true  )

inline

Generate indices for k-fold cross-validation.

Generates indices for splitting data into k folds.

Parameters

n	Data size
k	Number of folds
shuffle	Whether to shuffle (default: true)

Returns

Vector of indices belonging to each fold

Exceptions

std::invalid_argument

If k is less than 2 or k exceeds n

Definition at line 250 of file model_selection.hpp.

create_missing_indicator()

std::vector< std::vector< double > > statcpp::create_missing_indicator ( const std::vector< std::vector< double > > &  data )

inline

Create missing indicator variables.

Creates an indicator variable matrix where each element is 1.0 if missing and 0.0 if observed.

Parameters

data	Input data (rows: observations, columns: variables)

Returns

std::vector<std::vector<double>> Missing indicator matrix (1 = missing, 0 = observed)

Definition at line 179 of file missing_data.hpp.

cross_validate_linear()

cv_result statcpp::cross_validate_linear ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, std::size_t  k = 5  )

inline

Perform k-fold cross-validation for multiple regression model.

Splits data into specified number of folds and evaluates model prediction performance through cross-validation.

Parameters

X	Predictor matrix (each row is one sample)
y	Response variable vector
k	Number of folds (default: 5)

Returns

Cross-validation result

Exceptions

std::invalid_argument

If X and y have different sizes

Definition at line 294 of file model_selection.hpp.

cumulative_frequency() [1/2]

template<typename Iterator >

auto statcpp::cumulative_frequency	(	Iterator	first,
		Iterator	last
	)		-> std::vector<std::pair<typename std::iterator_traits<Iterator>::value_type, std::size_t>>

Return cumulative frequency (for sorted values)

Calculates the cumulative frequency up to each value. Results are sorted in ascending order by value.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator
last	Ending iterator

Returns

Vector of (value, cumulative frequency) pairs

Definition at line 305 of file frequency_distribution.hpp.

cumulative_frequency() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::cumulative_frequency	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> std::vector<std::pair<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>, std::size_t>>

Cumulative frequency with projection.

Returns the cumulative frequency of results after applying a projection function to each element. Results are sorted in ascending order by value.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator
last	Ending iterator
proj	Projection function

Returns

Vector of (value, cumulative frequency) pairs

Definition at line 346 of file frequency_distribution.hpp.

cumulative_relative_frequency() [1/2]

template<typename Iterator >

auto statcpp::cumulative_relative_frequency	(	Iterator	first,
		Iterator	last
	)		-> std::vector<std::pair<typename std::iterator_traits<Iterator>::value_type, double>>

Return cumulative relative frequency (for sorted values)

Calculates the cumulative relative frequency up to each value. Results are sorted in ascending order by value.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator
last	Ending iterator

Returns

Vector of (value, cumulative relative frequency) pairs

Definition at line 390 of file frequency_distribution.hpp.

cumulative_relative_frequency() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::cumulative_relative_frequency	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> std::vector<std::pair<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>, double>>

Cumulative relative frequency with projection.

Returns the cumulative relative frequency of results after applying a projection function to each element. Results are sorted in ascending order by value.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator
last	Ending iterator
proj	Projection function

Returns

Vector of (value, cumulative relative frequency) pairs

Definition at line 427 of file frequency_distribution.hpp.

cut_dendrogram()

std::vector< std::size_t > statcpp::cut_dendrogram ( const std::vector< dendrogram_node > &  dendrogram, std::size_t  n_data, std::size_t  k  )

inline

Extract k clusters from dendrogram.

Cuts the dendrogram to extract k clusters.

Parameters

dendrogram	Dendrogram
n_data	Number of data points
k	Number of clusters

Returns

Cluster labels

Exceptions

std::invalid_argument

If k is invalid

Definition at line 425 of file clustering.hpp.

cv_lasso()

std::pair< double, std::vector< double > > statcpp::cv_lasso ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, const std::vector< double > &  lambda_grid, std::size_t  k = 5  )

inline

Select optimal lambda for Lasso regression using cross-validation.

Performs k-fold cross-validation for a grid of lambda values and selects the lambda with minimum cross-validation error.

Parameters

X	Predictor matrix (each row is one sample)
y	Response variable vector
lambda_grid	Vector of lambda values to evaluate
k	Number of folds (default: 5)

Returns

Pair of optimal lambda and cross-validation errors for each lambda

Definition at line 905 of file model_selection.hpp.

cv_ridge()

std::pair< double, std::vector< double > > statcpp::cv_ridge ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, const std::vector< double > &  lambda_grid, std::size_t  k = 5  )

inline

Select optimal lambda for Ridge regression using cross-validation.

Performs k-fold cross-validation for a grid of lambda values and selects the lambda with minimum cross-validation error.

Parameters

X	Predictor matrix (each row is one sample)
y	Response variable vector
lambda_grid	Vector of lambda values to evaluate
k	Number of folds (default: 5)

Returns

Pair of optimal lambda and cross-validation errors for each lambda

Definition at line 837 of file model_selection.hpp.

d_to_r()

double statcpp::d_to_r ( double  d )

inline

Convert Cohen's d to correlation coefficient.

Parameters

d

Cohen's d

Returns

Correlation coefficient

Definition at line 260 of file effect_size.hpp.

detect_outliers_iqr()

template<typename Iterator >

outlier_detection_result statcpp::detect_outliers_iqr	(	Iterator	first,
		Iterator	last,
		double	k = 1.5
	)

Outlier detection using IQR method (Tukey's Fences)

Detects outliers using the interquartile range (Tukey's Fences).

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range
k	Fence multiplier (default: 1.5, use 3.0 for extreme outliers)

Returns

Outlier detection result

Exceptions

std::invalid_argument

If range is empty

Note

Standard box plots use k=1.5.

Definition at line 130 of file robust.hpp.

detect_outliers_modified_zscore()

template<typename Iterator >

outlier_detection_result statcpp::detect_outliers_modified_zscore	(	Iterator	first,
		Iterator	last,
		double	threshold = 3.5
	)

Outlier detection using Modified Z-score.

Detects outliers using MAD-based Modified Z-score (more robust).

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range
threshold	Modified Z-score threshold (default: 3.5)

Returns

Outlier detection result

Exceptions

std::invalid_argument

If range is empty or MAD is zero

Note

More robust than standard Z-score. Less affected by outliers.

Definition at line 239 of file robust.hpp.

detect_outliers_zscore()

template<typename Iterator >

outlier_detection_result statcpp::detect_outliers_zscore	(	Iterator	first,
		Iterator	last,
		double	threshold = 3.0
	)

Outlier detection using Z-score.

Detects outliers using Z-score (standardized values).

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range
threshold	Z-score threshold (default: 3.0)

Returns

Outlier detection result

Exceptions

std::invalid_argument

If range has less than 2 elements or standard deviation is zero

Note

Assumes normal distribution. Sensitive to outliers.

Definition at line 190 of file robust.hpp.

dffits()

std::vector< double > statcpp::dffits ( const std::vector< double > &  residuals, const std::vector< double > &  hat_values, double  mse  )

inline

Calculate DFFITS.

Calculates DFFITS to measure the influence of each observation on predicted values.

Parameters

residuals	Residuals
hat_values	Leverage values (hat values)
mse	Mean squared error

Returns

DFFITS values

Exceptions

std::invalid_argument

If parameters are invalid

Note

|DFFITS_i| > 2*sqrt(p/n) indicates the observation is influential.

Definition at line 418 of file robust.hpp.

diagnose_missing_mechanism()

missing_mechanism statcpp::diagnose_missing_mechanism ( const std::vector< std::vector< double > > &  data )

inline

Simple diagnosis of missing mechanism.

Diagnoses the missing mechanism (MCAR, MAR, MNAR) of the data. Internally performs Little's MCAR test and estimates the missing mechanism based on the result.

Note

Distinguishing between MAR and MNAR is difficult with observed data alone, so if MCAR is rejected, it is conservatively classified as MAR.

Parameters

data	2D data for diagnosis (rows: observations, columns: variables)

Returns

missing_mechanism Estimated missing mechanism

Definition at line 330 of file missing_data.hpp.

diff()

template<typename Iterator >

std::vector< double > statcpp::diff	(	Iterator	first,
		Iterator	last,
		std::size_t	order = 1
	)

Difference series (first-order or d-th order differencing)

Calculates the difference of time series data.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
order	Differencing order (default: 1)

Returns

Vector of differenced series

Exceptions

std::invalid_argument

If data is insufficient for the differencing order

Definition at line 417 of file time_series.hpp.

discrete_uniform_cdf()

double statcpp::discrete_uniform_cdf ( std::int64_t  k, std::int64_t  a, std::int64_t  b  )

inline

Discrete uniform distribution cumulative distribution function (CDF)

Parameters

k	Upper bound
a	Lower bound (inclusive)
b	Upper bound (inclusive)

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If a > b

Definition at line 864 of file discrete_distributions.hpp.

discrete_uniform_pmf()

double statcpp::discrete_uniform_pmf ( std::int64_t  k, std::int64_t  a, std::int64_t  b  )

inline

Discrete uniform distribution probability mass function (PMF)

P(X = k) = 1 / (b - a + 1) for a <= k <= b

Parameters

k	Value
a	Lower bound (inclusive)
b	Upper bound (inclusive)

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If a > b

Definition at line 844 of file discrete_distributions.hpp.

discrete_uniform_quantile()

std::int64_t statcpp::discrete_uniform_quantile ( double  p, std::int64_t  a, std::int64_t  b  )

inline

Discrete uniform distribution quantile function.

Parameters

p	Cumulative probability
a	Lower bound (inclusive)
b	Upper bound (inclusive)

Returns

Smallest k such that P(X <= k) >= p

Exceptions

std::invalid_argument

If a > b or p is outside [0, 1]

Definition at line 887 of file discrete_distributions.hpp.

discrete_uniform_rand() [1/2]

std::int64_t statcpp::discrete_uniform_rand ( std::int64_t  a, std::int64_t  b  )

inline

Discrete uniform distribution random number generation (using default engine)

Parameters

a	Lower bound (inclusive)
b	Upper bound (inclusive)

Returns

Generated random number

Definition at line 929 of file discrete_distributions.hpp.

discrete_uniform_rand() [2/2]

template<typename Engine = default_random_engine>

std::int64_t statcpp::discrete_uniform_rand	(	std::int64_t	a,
		std::int64_t	b,
		Engine &	engine
	)

Discrete uniform distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

a	Lower bound (inclusive)
b	Upper bound (inclusive)
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If a > b

Definition at line 913 of file discrete_distributions.hpp.

drop_duplicates()

template<typename T >

std::vector< T > statcpp::drop_duplicates

(

const std::vector< T > &

data

)

Drop duplicates.

Template Parameters

T

Data type

Parameters

data	Data vector

Returns

Data with duplicates removed

Definition at line 723 of file data_wrangling.hpp.

dropna() [1/2]

template<typename T >

std::vector< std::vector< T > > statcpp::dropna

(

const std::vector< std::vector< T > > &

data

)

Drop rows containing NA.

Template Parameters

T

Data type

Parameters

data	2-dimensional data

Returns

Data containing only rows without NA

Definition at line 56 of file data_wrangling.hpp.

dropna() [2/2]

template<typename T >

std::vector< T > statcpp::dropna

(

const std::vector< T > &

data

)

Drop NA from a 1-dimensional vector.

Template Parameters

T

Data type

Parameters

data	1-dimensional data

Returns

Data without NA

Definition at line 85 of file data_wrangling.hpp.

dunnett_posthoc()

posthoc_result statcpp::dunnett_posthoc ( const one_way_anova_result &  anova_result, std::size_t  control_group = 0, double  alpha = 0.05  )

inline

Perform Dunnett's test for multiple comparisons against a control group.

Performs comparisons between a specified control group and all other groups as a post-hoc test following one-way ANOVA. Uses Bonferroni approximation.

Parameters

anova_result	Result from one-way ANOVA
control_group	Index of the control group (default: 0)
alpha	Significance level (default: 0.05)

Returns

posthoc_result Post-hoc comparison results

Exceptions

std::invalid_argument	If alpha is outside the range (0, 1)
std::invalid_argument	If control_group is an invalid index

Definition at line 514 of file anova.hpp.

elastic_net_regression()

regularized_regression_result statcpp::elastic_net_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, double  lambda, double  alpha = 0.5, bool  standardize = true, std::size_t  max_iter = 1000, double  tol = 1e-6  )

inline

Perform Elastic Net regression (L1 + L2 regularization)

Solves Elastic Net regression using coordinate descent. Combines L1 and L2 penalties, achieving both Lasso's variable selection and Ridge's stability.

Parameters

X	Predictor matrix (each row is one sample, no intercept column)
y	Response variable vector
lambda	Regularization parameter (>= 0)
alpha	L1 penalty ratio (0 = Ridge, 1 = Lasso, default: 0.5)
standardize	Whether to standardize data (default: true)
max_iter	Maximum number of iterations (default: 1000)
tol	Convergence tolerance (default: 1e-6)

Returns

Regularized regression result

Exceptions

std::invalid_argument

If lambda is negative, alpha is outside [0,1], data is empty, or X and y have different sizes

Definition at line 708 of file model_selection.hpp.

erf()

double statcpp::erf ( double  x )

inline

Error function.

Computes the error function erf(x).

Parameters

x

Argument

Returns

erf(x)

Note

Reference: Abramowitz and Stegun, 7.1.26

Uses Horner's method approximation

Definition at line 364 of file special_functions.hpp.

erfc()

double statcpp::erfc ( double  x )

inline

Complementary error function.

Computes the complementary error function erfc(x) = 1 - erf(x).

Parameters

x

Argument

Returns

erfc(x)

Definition at line 377 of file special_functions.hpp.

eta_squared() [1/2]

double statcpp::eta_squared ( const one_way_anova_result &  result )

inline

Calculate Eta-squared for one-way ANOVA.

Effect size measure indicating the proportion of total variation accounted for by between-group variation.

Parameters

result

Result from one-way ANOVA

Returns

double Eta-squared value (range 0 to 1)

Definition at line 828 of file anova.hpp.

eta_squared() [2/2]

double statcpp::eta_squared ( double  ss_effect, double  ss_total  )

inline

Calculate eta-squared from F-test.

Calculates the effect size from the sum of squares for effect and total.

Parameters

ss_effect	Sum of squares for effect
ss_total	Total sum of squares

Returns

Eta-squared

Exceptions

std::invalid_argument

If ss_total is not positive

Definition at line 296 of file effect_size.hpp.

euclidean_distance() [1/3]

double statcpp::euclidean_distance ( const std::vector< double > &  a, const std::vector< double > &  b  )

inline

Euclidean distance.

Computes the Euclidean distance between two vectors.

Parameters

a	First vector
b	Second vector

Returns

Euclidean distance

Exceptions

std::invalid_argument

If vector dimensions mismatch

Definition at line 39 of file clustering.hpp.

euclidean_distance() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::euclidean_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Euclidean distance (L2 norm)

Computes the Euclidean distance between two points in n-dimensional space: d(x, y) = sqrt(sum((x_i - y_i)^2))

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence

Returns

Euclidean distance

Exceptions

std::invalid_argument

if sequences have different lengths

Definition at line 31 of file distance_metrics.hpp.

euclidean_distance() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::euclidean_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Proj1	proj1,
		Proj2	proj2
	)

Euclidean distance with projection.

Definition at line 62 of file distance_metrics.hpp.

expm1_safe()

double statcpp::expm1_safe ( double  x )

inline

Safely compute exp(x) - 1 for small x.

Uses std::expm1 which is more accurate than exp(x) - 1 for small x

Parameters

x	Input value

Returns

exp(x) - 1

Definition at line 185 of file numerical_utils.hpp.

exponential_cdf()

double statcpp::exponential_cdf ( double  x, double  lambda = 1.0  )

inline

Exponential distribution cumulative distribution function (CDF)

F(x) = 1 - exp(-lambda*x)

Parameters

x	Random variable value
lambda	Rate parameter (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If lambda <= 0

Definition at line 263 of file continuous_distributions.hpp.

exponential_moving_average()

template<typename Iterator >

std::vector< double > statcpp::exponential_moving_average	(	Iterator	first,
		Iterator	last,
		double	alpha
	)

Exponential moving average.

Calculates the exponential moving average using smoothing parameter alpha.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
alpha	Smoothing parameter (0 < alpha <= 1)

Returns

Vector of exponential moving averages

Exceptions

std::invalid_argument

If range is empty or alpha is outside (0, 1]

Definition at line 374 of file time_series.hpp.

exponential_pdf()

double statcpp::exponential_pdf ( double  x, double  lambda = 1.0  )

inline

Exponential distribution probability density function (PDF)

f(x) = lambda * exp(-lambda*x) for x >= 0

Parameters

x	Random variable value
lambda	Rate parameter (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If lambda <= 0

Definition at line 244 of file continuous_distributions.hpp.

exponential_quantile()

double statcpp::exponential_quantile ( double  p, double  lambda = 1.0  )

inline

Exponential distribution quantile function.

Q(p) = -ln(1-p) / lambda

Parameters

p	Probability (0 <= p < 1)
lambda	Rate parameter (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If lambda <= 0 or p is outside [0, 1)

Definition at line 282 of file continuous_distributions.hpp.

exponential_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::exponential_rand	(	double	lambda,
		Engine &	engine
	)

Exponential distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

lambda	Rate parameter
engine	Random engine

Returns

Random number following exponential distribution

Exceptions

std::invalid_argument

If lambda <= 0

Definition at line 304 of file continuous_distributions.hpp.

exponential_rand() [2/2]

double statcpp::exponential_rand ( double  lambda = 1.0 )

inline

Exponential distribution random number generation (using default engine)

Parameters

lambda

Rate parameter (default: 1.0)

Returns

Random number following exponential distribution

Definition at line 319 of file continuous_distributions.hpp.

extract_complete_cases()

complete_case_result statcpp::extract_complete_cases ( const std::vector< std::vector< double > > &  data )

inline

Extract complete cases.

Extracts only rows without missing values (complete cases) from the dataset. This is also called listwise deletion.

Parameters

data	Input data (rows: observations, columns: variables)

Returns

complete_case_result Complete case analysis result

Definition at line 1063 of file missing_data.hpp.

f_cdf()

double statcpp::f_cdf ( double  x, double  df1, double  df2  )

inline

F-distribution cumulative distribution function (CDF)

Computed using the incomplete beta function. F(x) = I_{d1*x/(d1*x + d2)}(d1/2, d2/2)

Parameters

x	Random variable value
df1	First degrees of freedom
df2	Second degrees of freedom

Returns

Cumulative probability

Exceptions

std::invalid_argument

If df1 <= 0 or df2 <= 0

Definition at line 862 of file continuous_distributions.hpp.

f_pdf()

double statcpp::f_pdf ( double  x, double  df1, double  df2  )

inline

F-distribution probability density function (PDF)

f(x) = sqrt((d1*x)^d1 * d2^d2 / (d1*x + d2)^(d1+d2)) / (x * B(d1/2, d2/2))

Parameters

x	Random variable value
df1	First degrees of freedom
df2	Second degrees of freedom

Returns

Probability density

Exceptions

std::invalid_argument

If df1 <= 0 or df2 <= 0

Definition at line 832 of file continuous_distributions.hpp.

f_quantile()

double statcpp::f_quantile ( double  p, double  df1, double  df2  )

inline

F-distribution quantile function (Newton-Raphson method)

Parameters

p	Probability (0 <= p <= 1)
df1	First degrees of freedom
df2	Second degrees of freedom

Returns

Quantile

Exceptions

std::invalid_argument

If df1 <= 0, df2 <= 0, or p is outside [0, 1]

Note

Uses Newton-Raphson iteration with tolerance eps = 1e-10 and maximum 50 iterations. If the iteration does not converge within the maximum number of iterations, the best approximation so far is returned (no exception is thrown). For interior points (0 < p < 1), the result is a finite value. Boundary values p = 0 or p = 1 may return +/-infinity as per the distribution definition. In practice, convergence is achieved for all typical input ranges.

Definition at line 893 of file continuous_distributions.hpp.

f_rand() [1/2]

double statcpp::f_rand ( double  df1, double  df2  )

inline

F-distribution random number generation (using default engine)

Parameters

df1	First degrees of freedom
df2	Second degrees of freedom

Returns

Random number following F-distribution

Definition at line 976 of file continuous_distributions.hpp.

f_rand() [2/2]

template<typename Engine = default_random_engine>

double statcpp::f_rand	(	double	df1,
		double	df2,
		Engine &	engine
	)

F-distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

df1	First degrees of freedom
df2	Second degrees of freedom
engine	Random engine

Returns

Random number following F-distribution

Exceptions

std::invalid_argument

If df1 <= 0 or df2 <= 0

Definition at line 957 of file continuous_distributions.hpp.

f_test()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::f_test	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

F-test (variance comparison)

Tests whether the variances of two samples are equal.

Template Parameters

Iterator1	Input iterator type for first sample
Iterator2	Input iterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (F-statistic, p-value, df=df1, df2=df2)

Exceptions

std::invalid_argument

If either sample has less than 2 elements or second sample variance is zero

Definition at line 634 of file parametric_tests.hpp.

fillna()

template<typename T >

std::vector< T > statcpp::fillna	(	const std::vector< T > &	data,
		T	fill_value
	)

Fill NA with a specified value.

Template Parameters

T

Data type

Parameters

data	Data vector
fill_value	Value to fill

Returns

Data with NA filled

Definition at line 110 of file data_wrangling.hpp.

fillna_bfill()

std::vector< double > statcpp::fillna_bfill ( const std::vector< double > &  data )

inline

Fill NA with backward fill.

Parameters

data	Data vector

Returns

Data with NA filled with backward values

Definition at line 196 of file data_wrangling.hpp.

fillna_ffill()

std::vector< double > statcpp::fillna_ffill ( const std::vector< double > &  data )

inline

Fill NA with forward fill.

Parameters

data	Data vector

Returns

Data with NA filled with forward values

Definition at line 176 of file data_wrangling.hpp.

fillna_interpolate()

std::vector< double > statcpp::fillna_interpolate ( const std::vector< double > &  data )

inline

Fill NA with linear interpolation.

Parameters

data	Data vector

Returns

Data with NA filled with linear interpolation

Definition at line 216 of file data_wrangling.hpp.

fillna_mean()

std::vector< double > statcpp::fillna_mean ( const std::vector< double > &  data )

inline

Fill NA with mean.

Parameters

data	Data vector

Returns

Data with NA filled with mean

Definition at line 128 of file data_wrangling.hpp.

fillna_median()

std::vector< double > statcpp::fillna_median ( const std::vector< double > &  data )

inline

Fill NA with median.

Parameters

data	Data vector

Returns

Data with NA filled with median

Definition at line 152 of file data_wrangling.hpp.

filter()

template<typename T , typename Predicate >

std::vector< T > statcpp::filter	(	const std::vector< T > &	data,
		Predicate	pred
	)

Filter elements that match a condition.

Template Parameters

T	Data type
Predicate	Predicate type

Parameters

data	Data vector
pred	Predicate function

Returns

Vector of elements satisfying the condition

Definition at line 266 of file data_wrangling.hpp.

filter_range()

template<typename T >

std::vector< T > statcpp::filter_range	(	const std::vector< T > &	data,
		T	min_val,
		T	max_val
	)

Filter values within a range.

Template Parameters

T

Data type

Parameters

data	Data vector
min_val	Minimum value
max_val	Maximum value

Returns

Vector of values within the range

Definition at line 310 of file data_wrangling.hpp.

filter_rows()

template<typename T , typename Predicate >

std::vector< std::vector< T > > statcpp::filter_rows	(	const std::vector< std::vector< T > > &	data,
		Predicate	pred
	)

Filter rows that match a condition (2-dimensional)

Template Parameters

T	Data type
Predicate	Predicate type

Parameters

data	2-dimensional data
pred	Predicate function

Returns

Data containing only rows satisfying the condition

Definition at line 288 of file data_wrangling.hpp.

find_tipping_point()

tipping_point_result statcpp::find_tipping_point ( const std::vector< double > &  data, double  threshold = 0.0, double  delta_min = -5.0, double  delta_max = 5.0, std::size_t  n_points = 100  )

inline

Tipping point analysis.

Searches for the critical point (tipping point) where the estimated mean crosses the specified threshold. This allows assessment of how extreme the MNAR assumption must be to change conclusions.

Parameters

data	1D data for analysis
threshold	Threshold (e.g., null hypothesis value)
delta_min	Minimum delta value to search (default: -5.0)
delta_max	Maximum delta value to search (default: 5.0)
n_points	Number of search points (default: 100)

Returns

tipping_point_result Tipping point analysis result

Definition at line 985 of file missing_data.hpp.

fisher_exact_test()

test_result statcpp::fisher_exact_test ( std::uint64_t  a, std::uint64_t  b, std::uint64_t  c, std::uint64_t  d, alternative_hypothesis  alt = alternative_hypothesis::two_sided  )

inline

Perform Fisher's exact test (2x2 contingency table)

Tests whether row and column variables are independent in a 2x2 contingency table. Uses exact probability calculation based on hypergeometric distribution, applicable even when expected frequencies are small.

Contingency table format:

      | Col1 | Col2 | Row Total
Row1  |  a   |  b   |   a+b
Row2  |  c   |  d   |   c+d
Col   | a+c  | b+d  |   n

Parameters

a	Frequency of cell (1,1)
b	Frequency of cell (1,2)
c	Frequency of cell (2,1)
d	Frequency of cell (2,2)
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result containing odds ratio, p-value, and degrees of freedom (NaN)

Note

Null hypothesis: Row and column variables are independent (odds ratio = 1)

For two-sided test, sums probabilities of all tables with probability less than or equal to observed

If b or c is zero, odds ratio is infinity

Definition at line 925 of file nonparametric_tests.hpp.

five_number_summary() [1/2]

template<typename Iterator >

five_number_summary_result statcpp::five_number_summary	(	Iterator	first,
		Iterator	last
	)

Return five-number summary.

Calculates five-number summary (min, Q1, median, Q3, max) from sorted range.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of sorted range
last	End of sorted range

Returns

Five-number summary

Exceptions

std::invalid_argument

If range is empty

Note

Provides basic statistics needed for box plot visualization.

Definition at line 340 of file order_statistics.hpp.

five_number_summary() [2/2]

template<typename Iterator , typename Projection >

five_number_summary_result statcpp::five_number_summary	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Return five-number summary with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of sorted range
last	End of sorted range
proj	Projection function

Returns

Five-number summary

Exceptions

std::invalid_argument

If range is empty

Definition at line 373 of file order_statistics.hpp.

frequency_count() [1/2]

template<typename Iterator >

auto statcpp::frequency_count	(	Iterator	first,
		Iterator	last
	)		-> std::unordered_map<typename std::iterator_traits<Iterator>::value_type, std::size_t>

Return frequency for each value (unordered_map version, fast)

Counts the number of occurrences of each value. Sort order is not guaranteed, but operates faster.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator
last	Ending iterator

Returns

Map of values and their frequencies

Definition at line 178 of file frequency_distribution.hpp.

frequency_count() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::frequency_count	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> std::unordered_map<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>, std::size_t>

Frequency count with projection.

Returns the frequency of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator
last	Ending iterator
proj	Projection function

Returns

Map of values and their frequencies

Definition at line 203 of file frequency_distribution.hpp.

frequency_table() [1/2]

template<typename Iterator >

auto statcpp::frequency_table	(	Iterator	first,
		Iterator	last
	)		-> frequency_table_result<typename std::iterator_traits<Iterator>::value_type>

Create frequency table (returned with sorted keys)

Calculates frequency, relative frequency, cumulative frequency, and cumulative relative frequency for each value. Results are sorted in ascending order by key.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator
last	Ending iterator

Returns

Frequency table result

Definition at line 74 of file frequency_distribution.hpp.

frequency_table() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::frequency_table	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> frequency_table_result<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>>

Frequency table with projection.

Creates a frequency table of the results after applying a projection function to each element. Results are sorted in ascending order by key.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator
last	Ending iterator
proj	Projection function

Returns

Frequency table result

Definition at line 125 of file frequency_distribution.hpp.

gamma_cdf()

double statcpp::gamma_cdf ( double  x, double  shape, double  rate = 1.0  )

inline

Gamma distribution cumulative distribution function (CDF)

F(x) = P(alpha, beta*x) (regularized lower incomplete gamma function)

Parameters

x	Random variable value
shape	Shape parameter alpha
rate	Rate parameter beta (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If shape <= 0 or rate <= 0

Definition at line 369 of file continuous_distributions.hpp.

gamma_pdf()

double statcpp::gamma_pdf ( double  x, double  shape, double  rate = 1.0  )

inline

Gamma distribution probability density function (PDF)

f(x) = (beta^alpha / Gamma(alpha)) * x^(alpha-1) * exp(-beta*x) for x > 0 Parameters: shape = alpha (k), rate = beta (1/theta)

Parameters

x	Random variable value
shape	Shape parameter alpha
rate	Rate parameter beta (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If shape <= 0 or rate <= 0

Definition at line 340 of file continuous_distributions.hpp.

gamma_quantile()

double statcpp::gamma_quantile ( double  p, double  shape, double  rate = 1.0  )

inline

Gamma distribution quantile function.

Parameters

p	Probability (0 <= p <= 1)
shape	Shape parameter alpha
rate	Rate parameter beta (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If shape <= 0, rate <= 0, or p is outside [0, 1]

Definition at line 391 of file continuous_distributions.hpp.

gamma_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::gamma_rand	(	double	shape,
		double	rate,
		Engine &	engine
	)

Gamma distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

shape	Shape parameter alpha
rate	Rate parameter beta
engine	Random engine

Returns

Random number following gamma distribution

Exceptions

std::invalid_argument

If shape <= 0 or rate <= 0

Definition at line 419 of file continuous_distributions.hpp.

gamma_rand() [2/2]

double statcpp::gamma_rand ( double  shape, double  rate = 1.0  )

inline

Gamma distribution random number generation (using default engine)

Parameters

shape	Shape parameter alpha
rate	Rate parameter beta (default: 1.0)

Returns

Random number following gamma distribution

Definition at line 439 of file continuous_distributions.hpp.

gammainc_lower()

double statcpp::gammainc_lower ( double  a, double  x  )

inline

Lower regularized incomplete gamma function.

Computes the lower regularized incomplete gamma function P(a, x) = gamma(a, x) / Gamma(a).

Parameters

a	Shape parameter (must be positive)
x	Upper limit of integration (must be non-negative)

Returns

P(a, x)

Exceptions

std::domain_error

If parameters are invalid

Note

Uses series expansion for x < a + 1, continued fraction for x >= a + 1

Definition at line 490 of file special_functions.hpp.

gammainc_lower_inv()

double statcpp::gammainc_lower_inv ( double  a, double  p  )

inline

Inverse lower regularized incomplete gamma function.

Computes x such that P(a, x) = p.

Parameters

a	Shape parameter (must be positive)
p	Probability value (must be in [0, 1])

Returns

x such that P(a, x) = p

Exceptions

std::domain_error

If parameters are invalid

Note

Uses Newton-Raphson iteration

Uses Wilson-Hilferty approximation for initial guess when a > 1

Definition at line 573 of file special_functions.hpp.

gammainc_upper()

double statcpp::gammainc_upper ( double  a, double  x  )

inline

Upper regularized incomplete gamma function.

Computes the upper regularized incomplete gamma function Q(a, x) = Gamma(a, x) / Gamma(a) = 1 - P(a, x).

Parameters

a	Shape parameter (must be positive)
x	Lower limit of integration (must be non-negative)

Returns

Q(a, x)

Exceptions

std::domain_error

If parameters are invalid

Definition at line 555 of file special_functions.hpp.

generate_lambda_grid()

std::vector< double > statcpp::generate_lambda_grid ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, std::size_t  n_lambda = 100, double  lambda_min_ratio = 0.0001  )

inline

Automatically generate lambda grid for regularized regression.

Calculates maximum lambda based on data and generates a grid of lambda values on a logarithmic scale.

Parameters

X	Predictor matrix (each row is one sample)
y	Response variable vector
n_lambda	Grid size (default: 100)
lambda_min_ratio	Ratio of lambda_min to lambda_max (default: 0.0001)

Returns

Vector of lambda values equally spaced on logarithmic scale

Definition at line 972 of file model_selection.hpp.

geometric_cdf()

double statcpp::geometric_cdf ( std::uint64_t  k, double  p  )

inline

Geometric distribution cumulative distribution function (CDF)

P(X <= k) = 1 - (1-p)^(k+1)

Parameters

k	Upper bound of number of failures
p	Probability of success in each trial

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If p is outside (0, 1]

Definition at line 346 of file discrete_distributions.hpp.

geometric_mean() [1/2]

template<typename Iterator >

double statcpp::geometric_mean	(	Iterator	first,
		Iterator	last
	)

Geometric mean.

Computes the geometric mean of elements in the range. All values must be positive.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Geometric mean

Exceptions

std::invalid_argument

If range is empty or if a value is zero or negative

Definition at line 449 of file basic_statistics.hpp.

geometric_mean() [2/2]

template<typename Iterator , typename Projection >

double statcpp::geometric_mean	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Geometric mean of projected values using a lambda expression.

Computes the geometric mean of the results after applying a projection function to each element. All values must be positive.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Geometric mean of projected values

Exceptions

std::invalid_argument

If range is empty or if a value is zero or negative

Definition at line 480 of file basic_statistics.hpp.

geometric_pmf()

double statcpp::geometric_pmf ( std::uint64_t  k, double  p  )

inline

Geometric distribution probability mass function (PMF)

P(X = k) = (1-p)^k * p X = Number of failures before first success (support: k = 0, 1, 2, ...)

Parameters

k	Number of failures
p	Probability of success in each trial

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If p is outside (0, 1]

Definition at line 326 of file discrete_distributions.hpp.

geometric_quantile()

std::uint64_t statcpp::geometric_quantile ( double  prob, double  p  )

inline

Geometric distribution quantile function (inverse CDF)

Parameters

prob	Cumulative probability
p	Probability of success in each trial

Returns

Smallest k such that P(X <= k) >= prob

Exceptions

std::invalid_argument

If prob is outside [0, 1] or p is outside (0, 1]

Definition at line 364 of file discrete_distributions.hpp.

geometric_rand() [1/2]

std::uint64_t statcpp::geometric_rand ( double  p )

inline

Geometric distribution random number generation (using default engine)

Parameters

p	Probability of success in each trial

Returns

Generated random number

Definition at line 408 of file discrete_distributions.hpp.

geometric_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::geometric_rand	(	double	p,
		Engine &	engine
	)

Geometric distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

p	Probability of success in each trial
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If p is outside (0, 1]

Definition at line 393 of file discrete_distributions.hpp.

geometric_stddev() [1/2]

template<typename Iterator >

double statcpp::geometric_stddev	(	Iterator	first,
		Iterator	last
	)

Geometric standard deviation.

Computes the exponential of the standard deviation of log-transformed data. GSD = exp(sigma_ln) where sigma_ln is the standard deviation of ln(x) Useful for measuring dispersion of data following a log-normal distribution.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Geometric standard deviation

Exceptions

std::invalid_argument

If the range is empty or values are non-positive

Definition at line 1515 of file dispersion_spread.hpp.

geometric_stddev() [2/2]

template<typename Iterator , typename Projection >

double statcpp::geometric_stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Geometric standard deviation (projection version)

Computes the geometric standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Geometric standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty or values are non-positive

Definition at line 1552 of file dispersion_spread.hpp.

get_duplicates()

template<typename T >

std::vector< T > statcpp::get_duplicates

(

const std::vector< T > &

data

)

Get duplicate values.

Template Parameters

T

Data type

Parameters

data	Data vector

Returns

Vector of duplicate values

Definition at line 760 of file data_wrangling.hpp.

get_random_engine()

default_random_engine & statcpp::get_random_engine ( )

inline

Singleton accessor for global random engine.

Returns a thread-local random engine. Each thread can generate independent random sequences, making it thread-safe.

Returns

Reference to thread-local random engine

Definition at line 31 of file random_engine.hpp.

glass_delta()

template<typename Iterator1 , typename Iterator2 >

double statcpp::glass_delta	(	Iterator1	control_first,
		Iterator1	control_last,
		Iterator2	treatment_first,
		Iterator2	treatment_last
	)

Glass's Delta (using control group's standard deviation)

Calculates the effect size using only the control group's standard deviation. Useful when the variances of the experimental and control groups differ substantially.

Template Parameters

Iterator1	RandomAccessIterator type for control group
Iterator2	RandomAccessIterator type for treatment group

Parameters

control_first	Beginning iterator of control group
control_last	Ending iterator of control group
treatment_first	Beginning iterator of treatment group
treatment_last	Ending iterator of treatment group

Returns

Glass's Delta

Exceptions

std::invalid_argument

If control group has fewer than 2 elements, treatment group is empty, or control group has zero variance

Definition at line 214 of file effect_size.hpp.

glm_fit()

glm_result statcpp::glm_fit ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, distribution_family  family = distribution_family::gaussian, link_function  link = link_function::identity, std::size_t  max_iter = 100, double  tol = 1e-8  )

inline

Fit a generalized linear model.

Estimates parameters of a generalized linear model using the IRLS (Iteratively Reweighted Least Squares) algorithm.

Parameters

X	Predictor matrix (intercept is added automatically)
y	Response variable vector
family	Distribution family (default: gaussian)
link	Link function (default: identity)
max_iter	Maximum number of iterations (default: 100)
tol	Convergence tolerance (default: 1e-8)

Returns

GLM estimation results

Exceptions

std::invalid_argument

If data is empty, X and Y sizes don't match, number of predictors is inconsistent, or number of observations is not greater than number of predictors

Note

If the IRLS algorithm does not converge within max_iter iterations, converged is set to false and coefficient_se, z_statistics, and p_values may contain NaN values. NaN indicates that the corresponding estimate is undefined due to numerical issues (not a bug). Always check glm_result::converged before using these fields.

Definition at line 401 of file glm.hpp.

group_by()

template<typename K , typename V >

group_result< K, V > statcpp::group_by	(	const std::vector< K > &	keys,
		const std::vector< V > &	values
	)

Group by.

Template Parameters

K	Key type
V	Value type

Parameters

keys	Vector of keys
values	Vector of values

Returns

Grouping result

Definition at line 494 of file data_wrangling.hpp.

group_count()

template<typename K >

aggregation_result< K > statcpp::group_count	(	const std::vector< K > &	keys,
		const std::vector< double > &	values
	)

Count per group.

Template Parameters

K

Key type

Parameters

keys	Vector of keys
values	Vector of values

Returns

Element count for each group

Definition at line 555 of file data_wrangling.hpp.

group_mean()

template<typename K >

aggregation_result< K > statcpp::group_mean	(	const std::vector< K > &	keys,
		const std::vector< double > &	values
	)

Mean per group.

Template Parameters

K

Key type

Parameters

keys	Vector of keys
values	Vector of values

Returns

Mean value for each group

Definition at line 515 of file data_wrangling.hpp.

group_sum()

template<typename K >

aggregation_result< K > statcpp::group_sum	(	const std::vector< K > &	keys,
		const std::vector< double > &	values
	)

Sum per group.

Template Parameters

K

Key type

Parameters

keys	Vector of keys
values	Vector of values

Returns

Sum for each group

Definition at line 535 of file data_wrangling.hpp.

harmonic_mean() [1/2]

template<typename Iterator >

double statcpp::harmonic_mean	(	Iterator	first,
		Iterator	last
	)

Harmonic mean.

Computes the harmonic mean of elements in the range. All values must be non-zero.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Harmonic mean

Exceptions

std::invalid_argument

If range is empty or if a value is zero

Note

The current zero-detection threshold uses std::numeric_limits<double>::min() (smallest positive normal double, ~2.2e-308). This catches subnormals and zero, but users working with intentionally small positive values near this threshold should be aware of potential false rejections. A future version may allow a user-specified threshold.

Definition at line 519 of file basic_statistics.hpp.

harmonic_mean() [2/2]

template<typename Iterator , typename Projection >

double statcpp::harmonic_mean	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Harmonic mean of projected values using a lambda expression.

Computes the harmonic mean of the results after applying a projection function to each element. All values must be non-zero.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Harmonic mean of projected values

Exceptions

std::invalid_argument

If range is empty or if a value is zero

Definition at line 555 of file basic_statistics.hpp.

has_converged()

bool statcpp::has_converged ( double  x_new, double  x_old, double  abs_tol = 1e-8, double  rel_tol = 1e-6  )

inline

Check for convergence using combined absolute and relative criteria.

Convergence criterion: |x_new - x_old| <= abs_tol + rel_tol * |x_old|

Parameters

x_new	New value
x_old	Old value
abs_tol	Absolute tolerance (default: 1e-8)
rel_tol	Relative tolerance (default: 1e-6)

Returns

true if converged

Definition at line 156 of file numerical_utils.hpp.

has_converged_abs()

bool statcpp::has_converged_abs ( double  x_new, double  x_old, double  tol = 1e-6  )

inline

Check for convergence based on absolute change.

Convergence criterion: |x_new - x_old| <= tol

Parameters

x_new	New value
x_old	Old value
tol	Tolerance (default: 1e-6)

Returns

true if converged

Definition at line 122 of file numerical_utils.hpp.

has_converged_rel()

bool statcpp::has_converged_rel ( double  x_new, double  x_old, double  tol = 1e-6  )

inline

Check for convergence based on relative change.

Convergence criterion: |x_new - x_old| / max(|x_old|, eps) <= tol

Parameters

x_new	New value
x_old	Old value
tol	Tolerance (default: 1e-6)

Returns

true if converged

Definition at line 138 of file numerical_utils.hpp.

hedges_correction_factor()

double statcpp::hedges_correction_factor ( double  df )

inline

Hedges' bias correction factor J.

Calculates the correction factor for small sample size bias.

Parameters

df	Degrees of freedom

Returns

Bias correction factor

Definition at line 133 of file effect_size.hpp.

hedges_g()

template<typename Iterator >

double statcpp::hedges_g	(	Iterator	first,
		Iterator	last,
		double	mu0
	)

Hedges' g (one-sample)

Calculates bias-corrected Cohen's d.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	Ending iterator
mu0	Population mean to compare against

Returns

Hedges' g

Exceptions

std::invalid_argument

If there are fewer than 2 elements

Definition at line 152 of file effect_size.hpp.

hedges_g_two_sample()

template<typename Iterator1 , typename Iterator2 >

double statcpp::hedges_g_two_sample	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Hedges' g (two-sample)

Calculates bias-corrected standardized mean difference between two groups.

Template Parameters

Iterator1	RandomAccessIterator type for first sample
Iterator2	RandomAccessIterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	Ending iterator of first sample
first2	Beginning iterator of second sample
last2	Ending iterator of second sample

Returns

Hedges' g

Exceptions

std::invalid_argument

If either sample has fewer than 2 elements

Definition at line 179 of file effect_size.hpp.

hierarchical_clustering()

std::vector< dendrogram_node > statcpp::hierarchical_clustering ( const std::vector< std::vector< double > > &  data, linkage_type  linkage = linkage_type::single  )

inline

Hierarchical clustering.

Performs hierarchical clustering and generates a dendrogram.

Parameters

data	Vector of data points
linkage	Linkage type (default: single)

Returns

Dendrogram

Exceptions

std::invalid_argument

If data is empty

Note

Has O(n^3) time complexity. Not suitable for large datasets.

Definition at line 302 of file clustering.hpp.

hodges_lehmann()

template<typename Iterator >

double statcpp::hodges_lehmann	(	Iterator	first,
		Iterator	last
	)

Hodges-Lehmann estimator.

Calculates the median of all pairwise averages (Walsh average).

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range

Returns

Hodges-Lehmann estimate

Exceptions

std::invalid_argument

If range is empty

Note

A robust location estimator. Less affected by outliers.

Definition at line 475 of file robust.hpp.

holm_correction()

std::vector< double > statcpp::holm_correction ( const std::vector< double > &  p_values )

inline

Holm correction (step-down Bonferroni method)

Corrects p-values for multiple testing using the Holm method. A step-down version of Bonferroni correction with higher power.

Parameters

p_values

Vector of original p-values

Returns

std::vector<double> Vector of corrected p-values

Definition at line 751 of file parametric_tests.hpp.

hypergeom_cdf()

double statcpp::hypergeom_cdf ( std::uint64_t  k, std::uint64_t  N, std::uint64_t  K, std::uint64_t  n  )

inline

Hypergeometric distribution cumulative distribution function (CDF)

Calculates P(X <= k).

Parameters

k	Upper bound of success draws
N	Population size
K	Number of success states in population
n	Number of draws

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 460 of file discrete_distributions.hpp.

hypergeom_pmf()

double statcpp::hypergeom_pmf ( std::uint64_t  k, std::uint64_t  N, std::uint64_t  K, std::uint64_t  n  )

inline

Hypergeometric distribution probability mass function (PMF)

P(X = k) = C(K, k) * C(N-K, n-k) / C(N, n)

Parameters

k	Number of success draws
N	Population size
K	Number of success states in population
n	Number of draws

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If parameters are invalid (K > N or n > N)

Definition at line 429 of file discrete_distributions.hpp.

hypergeom_quantile()

std::uint64_t statcpp::hypergeom_quantile ( double  p, std::uint64_t  N, std::uint64_t  K, std::uint64_t  n  )

inline

Hypergeometric distribution quantile function (inverse CDF)

Parameters

p	Cumulative probability
N	Population size
K	Number of success states in population
n	Number of draws

Returns

Smallest k such that P(X <= k) >= p

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 491 of file discrete_distributions.hpp.

hypergeom_rand() [1/2]

std::uint64_t statcpp::hypergeom_rand ( std::uint64_t  N, std::uint64_t  K, std::uint64_t  n  )

inline

Hypergeometric distribution random number generation (using default engine)

Parameters

N	Population size
K	Number of success states in population
n	Number of draws

Returns

Generated random number

Definition at line 568 of file discrete_distributions.hpp.

hypergeom_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::hypergeom_rand	(	std::uint64_t	N,
		std::uint64_t	K,
		std::uint64_t	n,
		Engine &	engine
	)

Hypergeometric distribution random number generation.

Uses direct sampling method (suitable for moderate n).

Template Parameters

Engine

Random engine type

Parameters

N	Population size
K	Number of success states in population
n	Number of draws
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 532 of file discrete_distributions.hpp.

impute_conditional_mean()

std::vector< double > statcpp::impute_conditional_mean ( const std::vector< std::vector< double > > &  data, std::size_t  target_col, const std::vector< std::size_t > &  predictor_cols  )

inline

Single imputation by conditional mean.

Imputes missing values with conditional mean using simple linear regression with predictor variables.

Parameters

data	Input data (rows: observations, columns: variables)
target_col	Column index for imputation target
predictor_cols	Column indices for predictor variables

Returns

std::vector<double> Values of target_col after imputation

Definition at line 375 of file missing_data.hpp.

in_range()

bool statcpp::in_range ( double  x, double  min_val, double  max_val  )

inline

Check if a value is in range [min_val, max_val].

Parameters

x	Value to check
min_val	Minimum value
max_val	Maximum value

Returns

true if min_val <= x <= max_val

Definition at line 215 of file numerical_utils.hpp.

incidence_rate_ratios()

std::vector< double > statcpp::incidence_rate_ratios ( const glm_result &  model )

inline

Calculate Incidence Rate Ratios.

Calculates incidence rate ratios from Poisson regression model coefficients.

Parameters

model

Fitted Poisson regression model

Returns

Vector of incidence rate ratios for each predictor (excluding intercept)

Exceptions

std::invalid_argument

If model is not Poisson regression

Definition at line 850 of file glm.hpp.

interpolate_at() [1/2]

template<typename Iterator >

double statcpp::interpolate_at	(	Iterator	first,
		std::size_t	n,
		double	p
	)

Linear interpolation at position.

Decomposes position p * (n-1) into integer part lo and fractional part frac, then performs linear interpolation.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of sorted range
n	Number of elements
p	Position (0.0 to 1.0)

Returns

Interpolated value

Note

Assumes sorted range.

Definition at line 66 of file order_statistics.hpp.

interpolate_at() [2/2]

template<typename Iterator , typename Projection >

double statcpp::interpolate_at	(	Iterator	first,
		std::size_t	n,
		double	p,
		Projection	proj
	)

Linear interpolation at position with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of sorted range
n	Number of elements
p	Position (0.0 to 1.0)
proj	Projection function

Returns

Interpolated value

Definition at line 96 of file order_statistics.hpp.

interpret_cohens_d()

effect_size_magnitude statcpp::interpret_cohens_d ( double  d )

inline

Interpret Cohen's d.

Determines the magnitude of effect size based on Cohen (1988) criteria.

Parameters

d

Cohen's d

Returns

Effect size magnitude

Definition at line 441 of file effect_size.hpp.

interpret_correlation()

effect_size_magnitude statcpp::interpret_correlation ( double  r )

inline

Interpret correlation coefficient.

Determines the strength of correlation based on Cohen (1988) criteria.

Parameters

r	Correlation coefficient

Returns

Effect size magnitude

Definition at line 458 of file effect_size.hpp.

interpret_eta_squared()

effect_size_magnitude statcpp::interpret_eta_squared ( double  eta2 )

inline

Interpret eta-squared.

Determines the magnitude of effect size based on Cohen (1988) criteria.

Parameters

eta2	Eta-squared

Returns

Effect size magnitude

Definition at line 475 of file effect_size.hpp.

iqr() [1/2]

template<typename Iterator >

double statcpp::iqr	(	Iterator	first,
		Iterator	last
	)

Interquartile range (accepts a sorted range)

Computes the difference between the third and first quartiles. Useful for measuring the spread of the middle 50% of the data.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Interquartile range (Q3 - Q1)

Exceptions

std::invalid_argument

If the range is empty

Definition at line 956 of file dispersion_spread.hpp.

iqr() [2/2]

template<typename Iterator , typename Projection >

double statcpp::iqr	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Interquartile range of projected values (projection results must be in sorted order)

Computes the interquartile range of results after applying a projection function to each element. Assumes projection results are in sorted order.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Interquartile range of projected values (Q3 - Q1)

Exceptions

std::invalid_argument

If the range is empty

Definition at line 982 of file dispersion_spread.hpp.

is_finite()

bool statcpp::is_finite ( double  x )

inline

Check if a value is finite (not infinity or NaN)

Parameters

x	Value to check

Returns

true if x is finite

Definition at line 88 of file numerical_utils.hpp.

is_na()

bool statcpp::is_na ( double  x )

inline

Check if a value is NA.

Parameters

x	Value to check

Returns

true if NA, false otherwise

Definition at line 45 of file data_wrangling.hpp.

is_zero()

bool statcpp::is_zero ( double  x, double  tol = default_abs_tol  )

inline

Check if a value is close to zero.

Parameters

x	Value to check
tol	Tolerance (default: 1e-12)

Returns

true if |x| <= tol

Definition at line 77 of file numerical_utils.hpp.

kahan_sum() [1/2]

template<typename Iterator >

double statcpp::kahan_sum	(	Iterator	first,
		Iterator	last
	)

Compute sum with Kahan summation algorithm.

Kahan summation reduces numerical error in summing a sequence of floating-point numbers. More accurate than naive summation for large sequences or when values vary widely in magnitude.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning of sequence
last	End of sequence

Returns

Sum of elements using Kahan algorithm

Definition at line 264 of file numerical_utils.hpp.

kahan_sum() [2/2]

template<typename Iterator , typename Proj >

double statcpp::kahan_sum	(	Iterator	first,
		Iterator	last,
		Proj	proj
	)

Compute sum with Kahan summation algorithm (with projection)

Definition at line 284 of file numerical_utils.hpp.

kaplan_meier()

kaplan_meier_result statcpp::kaplan_meier ( const std::vector< double > &  times, const std::vector< bool > &  events  )

inline

Estimate Kaplan-Meier survival curve.

Estimates the survival curve from survival time data including censored observations. Calculates standard errors using Greenwood's formula and provides 95% confidence intervals.

Parameters

times	Vector of observation times
events	Event occurrence flags (true = event occurred, false = censored)

Returns

Kaplan-Meier estimation result

Exceptions

std::invalid_argument

If times and events have different sizes or data is empty

Definition at line 54 of file survival.hpp.

kendall_tau() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::kendall_tau	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Kendall's rank correlation coefficient (tau-b)

Computes Kendall's rank correlation coefficient (tau-b) of two variables. This version accounts for ties. tau_b = (concordant - discordant) / sqrt((n0 - tie_x) * (n0 - tie_y))

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Kendall's tau-b (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 735 of file correlation_covariance.hpp.

kendall_tau() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::kendall_tau	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Kendall's rank correlation coefficient (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Kendall's tau-b (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 829 of file correlation_covariance.hpp.

kmeans()

kmeans_result statcpp::kmeans ( const std::vector< std::vector< double > > &  data, std::size_t  k, std::size_t  max_iter = 100, double  tol = 1e-6  )

inline

K-means clustering.

Performs clustering using the K-means algorithm.

Parameters

data	Vector of data points
k	Number of clusters
max_iter	Maximum number of iterations (default: 100)
tol	Convergence tolerance (default: 1e-6)

Returns

Clustering result

Exceptions

std::invalid_argument

If data is empty, k is 0, or k exceeds number of data points

Definition at line 168 of file clustering.hpp.

kmeans_plusplus_init()

std::vector< std::vector< double > > statcpp::kmeans_plusplus_init ( const std::vector< std::vector< double > > &  data, std::size_t  k  )

inline

K-means++ initialization.

Selects initial cluster centroids using the K-means++ algorithm.

Parameters

data	Vector of data points
k	Number of clusters

Returns

Initial cluster centroids

Note

Arthur & Vassilvitskii (2007) "k-means++: the advantages of careful seeding"

Definition at line 101 of file clustering.hpp.

kruskal_wallis_test()

test_result statcpp::kruskal_wallis_test ( const std::vector< std::vector< double > > &  groups )

inline

Perform Kruskal-Wallis test (k-sample)

Tests whether three or more independent samples come from the same distribution. The nonparametric version of one-way ANOVA that does not assume normal distribution. Uses chi-square approximation for p-value calculation.

Parameters

groups

Vector of vectors containing data for each group

Returns

test_result Test result containing H statistic, p-value, and degrees of freedom (k-1)

Exceptions

std::invalid_argument	If there are fewer than 2 groups
std::invalid_argument	If any group is empty

Note

Null hypothesis: All groups are drawn from the same distribution

Larger H statistic indicates greater differences between groups

Definition at line 805 of file nonparametric_tests.hpp.

ks_test_normal()

template<typename Iterator >

test_result statcpp::ks_test_normal	(	Iterator	first,
		Iterator	last
	)

Perform Kolmogorov-Smirnov test for normality (deprecated)

Deprecated:

Use lilliefors_test() instead. This function will be removed in a future version. The implementation is actually a Lilliefors test (parameters estimated from data), not a standard KS test with known parameters.

Definition at line 372 of file nonparametric_tests.hpp.

kurtosis() [1/4]

template<typename Iterator >

double statcpp::kurtosis	(	Iterator	first,
		Iterator	last
	)

Calculate kurtosis (alias for sample_kurtosis)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Sample kurtosis value

Definition at line 635 of file shape_of_distribution.hpp.

kurtosis() [2/4]

template<typename Iterator >

double statcpp::kurtosis	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate kurtosis (precomputed mean version)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Sample kurtosis value

Definition at line 650 of file shape_of_distribution.hpp.

kurtosis() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate kurtosis (projection version)

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Sample kurtosis value

Definition at line 669 of file shape_of_distribution.hpp.

kurtosis() [4/4]

template<typename Iterator , typename Projection >

double statcpp::kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate kurtosis (projection version, precomputed mean)

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample kurtosis value

Definition at line 686 of file shape_of_distribution.hpp.

label_encode()

template<typename T >

label_encoding_result< T > statcpp::label_encode

(

const std::vector< T > &

data

)

Label encoding.

Template Parameters

T

Data type

Parameters

data	Data vector

Returns

Label encoding result

Definition at line 969 of file data_wrangling.hpp.

lag()

template<typename Iterator >

std::vector< double > statcpp::lag	(	Iterator	first,
		Iterator	last,
		std::size_t	k
	)

Generate lag series.

Creates a lag series from time series data.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
k	Lag

Returns

Vector of lag series

Exceptions

std::invalid_argument

If lag exceeds data length

Definition at line 499 of file time_series.hpp.

lasso_regression()

regularized_regression_result statcpp::lasso_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, double  lambda, bool  standardize = true, std::size_t  max_iter = 1000, double  tol = 1e-6  )

inline

Perform Lasso regression (L1 regularization)

Solves Lasso regression using coordinate descent. L1 penalty shrinks some coefficients exactly to zero, performing variable selection.

Parameters

X	Predictor matrix (each row is one sample, no intercept column)
y	Response variable vector
lambda	Regularization parameter (>= 0)
standardize	Whether to standardize data (default: true)
max_iter	Maximum number of iterations (default: 1000)
tol	Convergence tolerance (default: 1e-6)

Returns

Regularized regression result

Exceptions

std::invalid_argument

If lambda is negative, data is empty, or X and y have different sizes

Definition at line 582 of file model_selection.hpp.

lbeta()

double statcpp::lbeta ( double  a, double  b  )

inline

Log-beta function.

Computes the natural logarithm of the beta function.

Parameters

a	First parameter (must be positive)
b	Second parameter (must be positive)

Returns

log(B(a, b))

Exceptions

std::domain_error

If a or b is non-positive

Definition at line 166 of file special_functions.hpp.

levene_test()

test_result statcpp::levene_test ( const std::vector< std::vector< double > > &  groups )

inline

Perform Levene test (homogeneity of variance test)

Tests whether variances are equal across multiple groups. Uses the median-based Brown-Forsythe version, which is robust to departures from normality.

Parameters

groups

Vector of vectors containing data for each group

Returns

test_result Test result containing F statistic, p-value, and degrees of freedom

Exceptions

std::invalid_argument	If there are fewer than 2 groups
std::invalid_argument	If any group has fewer than 2 elements

Note

Null hypothesis: All groups have equal variance

Larger F statistic indicates greater heterogeneity of variance

Definition at line 397 of file nonparametric_tests.hpp.

lgamma()

double statcpp::lgamma ( double  x )

inline

Log-gamma function.

Computes the natural logarithm of the gamma function.

Parameters

x

Argument

Returns

log(Gamma(x))

Exceptions

std::domain_error

If x is a non-positive integer

Definition at line 100 of file special_functions.hpp.

lgamma_impl()

double statcpp::lgamma_impl ( double  x )

inline

Internal log-gamma function implementation.

Calculates log(Gamma(x)) using Lanczos approximation.

Parameters

x	Argument (must be positive or non-integer if negative)

Returns

log(Gamma(x))

Exceptions

std::domain_error

If x is a non-positive integer

Note

Reference: Numerical Recipes, Press et al.

Uses Lanczos coefficients for g=7

Definition at line 57 of file special_functions.hpp.

lilliefors_test()

template<typename Iterator >

test_result statcpp::lilliefors_test	(	Iterator	first,
		Iterator	last
	)

Perform Lilliefors test for normality.

Tests whether data follows a normal distribution. This is a Lilliefors test (not a standard KS test): parameters (mean, variance) are estimated from data, and the Lilliefors correction is applied to the p-value.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of range
last	Ending iterator of range

Returns

test_result Test result containing D statistic, p-value, and sample size

Exceptions

std::invalid_argument	If there are fewer than 2 elements
std::invalid_argument	If variance is zero

Note

Null hypothesis: Data follows a normal distribution

Larger D statistic indicates greater deviation from normal distribution

The current implementation uses an asymptotic approximation formula. Future versions may adopt more precise critical values (e.g., Dallal & Wilkinson 1986).

The Lilliefors asymptotic approximation may be imprecise for small samples (n < 20) or in extreme tail regions (very small p-values). For small samples, consider using the Shapiro-Wilk test as an alternative.

Definition at line 312 of file nonparametric_tests.hpp.

log1p_safe()

double statcpp::log1p_safe ( double  x )

inline

Safely compute log(1 + x) for small x.

Uses std::log1p which is more accurate than log(1 + x) for small x

Parameters

x	Input value

Returns

log(1 + x)

Definition at line 172 of file numerical_utils.hpp.

log1p_transform()

std::vector< double > statcpp::log1p_transform ( const std::vector< double > &  data )

inline

Logarithmic transformation (log1p: log(1 + x))

Parameters

data	Data vector

Returns

log1p-transformed data (values < -1 become NA)

Definition at line 346 of file data_wrangling.hpp.

log_binomial_coef()

double statcpp::log_binomial_coef ( std::uint64_t  n, std::uint64_t  k  )

inline

Calculate log binomial coefficient.

Calculates log(C(n, k)) = log(n! / (k! * (n-k)!))

Parameters

n	Total number of elements
k	Number of elements to choose

Returns

Value of log(C(n, k))

Definition at line 49 of file discrete_distributions.hpp.

log_factorial()

double statcpp::log_factorial ( std::uint64_t  n )

inline

Calculate log factorial.

Parameters

n	Non-negative integer

Returns

Value of log(n!)

Definition at line 34 of file discrete_distributions.hpp.

log_transform()

std::vector< double > statcpp::log_transform ( const std::vector< double > &  data )

inline

Logarithmic transformation (natural logarithm)

Parameters

data	Data vector

Returns

Log-transformed data (values <= 0 become NA)

Definition at line 326 of file data_wrangling.hpp.

logarithmic_mean()

template<typename T1 , typename T2 >

double statcpp::logarithmic_mean	(	T1	a,
		T2	b
	)

Logarithmic Mean.

Computes the logarithmic mean of two positive values. LM(a, b) = (b - a) / (ln(b) - ln(a)) for a != b LM(a, a) = a

Template Parameters

T1	Type of first argument
T2	Type of second argument

Parameters

a	First value
b	Second value

Returns

Logarithmic mean

Exceptions

std::invalid_argument

If arguments are not positive

Definition at line 845 of file basic_statistics.hpp.

logistic_regression()

glm_result statcpp::logistic_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, std::size_t  max_iter = 100, double  tol = 1e-8  )

inline

Logistic regression.

Fits a generalized linear model using binomial distribution and logit link function.

Parameters

X	Predictor matrix (intercept is added automatically)
y	Response variable vector (range 0 to 1)
max_iter	Maximum number of iterations (default: 100)
tol	Convergence tolerance (default: 1e-8)

Returns

GLM estimation results

Exceptions

std::invalid_argument

If y is outside [0,1] range or X contains an intercept column

Definition at line 675 of file glm.hpp.

lognormal_cdf()

double statcpp::lognormal_cdf ( double  x, double  mu = 0.0, double  sigma = 1.0  )

inline

Log-normal distribution cumulative distribution function (CDF)

F(x) = Phi((ln(x) - mu) / sigma)

Parameters

x	Random variable value
mu	Log-mean (default: 0.0)
sigma	Log-standard deviation (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 1020 of file continuous_distributions.hpp.

lognormal_pdf()

double statcpp::lognormal_pdf ( double  x, double  mu = 0.0, double  sigma = 1.0  )

inline

Log-normal distribution probability density function (PDF)

f(x) = (1 / (x * sigma * sqrt(2*pi))) * exp(-(ln(x) - mu)^2 / (2*sigma^2))

Parameters

x	Random variable value
mu	Log-mean (default: 0.0)
sigma	Log-standard deviation (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 996 of file continuous_distributions.hpp.

lognormal_quantile()

double statcpp::lognormal_quantile ( double  p, double  mu = 0.0, double  sigma = 1.0  )

inline

Log-normal distribution quantile function.

Q(p) = exp(mu + sigma * Phi^(-1)(p))

Parameters

p	Probability (0 < p < 1)
mu	Log-mean (default: 0.0)
sigma	Log-standard deviation (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If sigma <= 0 or p is outside (0, 1)

Definition at line 1043 of file continuous_distributions.hpp.

lognormal_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::lognormal_rand	(	double	mu,
		double	sigma,
		Engine &	engine
	)

Log-normal distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

mu	Log-mean
sigma	Log-standard deviation
engine	Random engine

Returns

Random number following log-normal distribution

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 1067 of file continuous_distributions.hpp.

lognormal_rand() [2/2]

double statcpp::lognormal_rand ( double  mu = 0.0, double  sigma = 1.0  )

inline

Log-normal distribution random number generation (using default engine)

Parameters

mu	Log-mean (default: 0.0)
sigma	Log-standard deviation (default: 1.0)

Returns

Random number following log-normal distribution

Definition at line 1083 of file continuous_distributions.hpp.

logrank_test()

logrank_result statcpp::logrank_test ( const std::vector< double > &  times1, const std::vector< bool > &  events1, const std::vector< double > &  times2, const std::vector< bool > &  events2  )

inline

Log-rank test (comparison of two survival curves)

Tests whether the survival curves of two groups are equal. A nonparametric test that considers the risk set at each time point.

Parameters

times1	Observation times for group 1
events1	Event occurrence flags for group 1
times2	Observation times for group 2
events2	Event occurrence flags for group 2

Returns

Log-rank test result

Exceptions

std::invalid_argument

If times and events sizes don't match or data is empty

Definition at line 184 of file survival.hpp.

loocv_linear()

cv_result statcpp::loocv_linear ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y  )

inline

Perform leave-one-out cross-validation.

Performs cross-validation using each sample as test data one at a time.

Parameters

X	Predictor matrix (each row is one sample)
y	Response variable vector

Returns

Cross-validation result

Definition at line 366 of file model_selection.hpp.

mad()

template<typename Iterator >

double statcpp::mad	(	Iterator	first,
		Iterator	last
	)

Median Absolute Deviation (MAD)

Computes the median of absolute deviations from the median.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range

Returns

MAD value

Exceptions

std::invalid_argument

If range is empty

Note

Used as a robust estimator of variance.

Definition at line 42 of file robust.hpp.

mad_scaled()

template<typename Iterator >

double statcpp::mad_scaled	(	Iterator	first,
		Iterator	last
	)

Scaled MAD for normal distribution.

Computes MAD scaled to estimate standard deviation for normal distribution.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range

Returns

Scaled MAD value

Exceptions

std::invalid_argument

If range is empty

Note

Scale factor derivation: For standard normal N(0,1), the median of absolute deviations |X - 0| = |X| is the inverse of the normal quantile function at 0.75, approximately 0.6745. Therefore, to use MAD as an estimator of standard deviation sigma: sigma = MAD / 0.6745 = MAD * 1.4826

This factor is exact only when the data follows a normal distribution. For non-normal distributions, the standard deviation estimate using this factor is an approximation.

Definition at line 93 of file robust.hpp.

mae()

template<typename Iterator1 , typename Iterator2 >

double statcpp::mae	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2
	)

Mean Absolute Error (MAE)

Calculates the mean absolute error between actual and predicted values.

Template Parameters

Iterator1	RandomAccessIterator type for actual values
Iterator2	RandomAccessIterator type for predicted values

Parameters

first1	Beginning iterator of actual values
last1	End iterator of actual values
first2	Beginning iterator of predicted values

Returns

MAE

Exceptions

std::invalid_argument

If range is empty

Definition at line 207 of file time_series.hpp.

mahalanobis_distance()

double statcpp::mahalanobis_distance ( const std::vector< double > &  x, const std::vector< double > &  mean, const std::vector< std::vector< double > > &  cov_matrix  )

inline

Mahalanobis distance.

Computes the Mahalanobis distance between a point and a distribution. This accounts for correlations in the data and is scale-invariant.

For a point x and a distribution with mean μ and covariance matrix Σ: d(x, μ) = sqrt((x - μ)ᵀ Σ⁻¹ (x - μ))

Current implementation supports 2-dimensional data only.

Parameters

x	Point to measure distance from
mean	Mean of the distribution
cov_matrix	Covariance matrix (2x2)

Returns

Mahalanobis distance

Exceptions

std::invalid_argument

if dimensions mismatch or covariance matrix is singular

Definition at line 322 of file distance_metrics.hpp.

manhattan_distance() [1/3]

double statcpp::manhattan_distance ( const std::vector< double > &  a, const std::vector< double > &  b  )

inline

Manhattan distance.

Computes the Manhattan distance between two vectors.

Parameters

a	First vector
b	Second vector

Returns

Manhattan distance

Exceptions

std::invalid_argument

If vector dimensions mismatch

Definition at line 63 of file clustering.hpp.

manhattan_distance() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::manhattan_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Manhattan distance (L1 norm, taxicab distance)

Computes the Manhattan distance between two points: d(x, y) = sum(|x_i - y_i|)

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence

Returns

Manhattan distance

Exceptions

std::invalid_argument

if sequences have different lengths

Definition at line 108 of file distance_metrics.hpp.

manhattan_distance() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::manhattan_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Proj1	proj1,
		Proj2	proj2
	)

Manhattan distance with projection.

Definition at line 139 of file distance_metrics.hpp.

mann_whitney_u_test()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::mann_whitney_u_test	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided,
		bool	correct = true
	)

Perform Mann-Whitney U test (two-sample)

Tests whether two independent samples come from the same distribution. Also known as Wilcoxon rank-sum test, a nonparametric test that does not assume normal distribution. Uses normal approximation for p-value calculation.

Template Parameters

Iterator1	Iterator type for first sample
Iterator2	Iterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	Ending iterator of first sample
first2	Beginning iterator of second sample
last2	Ending iterator of second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result containing U1 statistic, p-value, and total sample size

Exceptions

std::invalid_argument

If either sample has fewer than 2 elements

Note

Null hypothesis: Two samples are drawn from the same distribution

U1 is calculated from the rank sum of the first sample

Definition at line 672 of file nonparametric_tests.hpp.

mape()

template<typename Iterator1 , typename Iterator2 >

double statcpp::mape	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2
	)

Mean Absolute Percentage Error (MAPE)

Calculates the mean absolute percentage error between actual and predicted values.

Template Parameters

Iterator1	RandomAccessIterator type for actual values
Iterator2	RandomAccessIterator type for predicted values

Parameters

first1	Beginning iterator of actual values
last1	End iterator of actual values
first2	Beginning iterator of predicted values

Returns

MAPE (percentage)

Exceptions

std::invalid_argument

If range is empty or all actual values are zero

Definition at line 285 of file time_series.hpp.

margin_of_error_mean() [1/2]

template<typename Iterator , typename Projection >

double statcpp::margin_of_error_mean	(	Iterator	first,
		Iterator	last,
		double	confidence,
		Projection	proj
	)

Calculate margin of error for mean (projection version)

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
confidence	Confidence level
proj	Projection function

Returns

Margin of error

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or there are fewer than 2 elements

Definition at line 499 of file estimation.hpp.

margin_of_error_mean() [2/2]

template<typename Iterator >

double statcpp::margin_of_error_mean	(	Iterator	first,
		Iterator	last,
		double	confidence = 0.95
	)

Calculate margin of error for mean.

MoE = t_{alpha/2, df} * SE

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
confidence	Confidence level (default: 0.95)

Returns

Margin of error

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or there are fewer than 2 elements

Definition at line 467 of file estimation.hpp.

margin_of_error_proportion()

double statcpp::margin_of_error_proportion ( std::size_t  successes, std::size_t  n, double  confidence = 0.95  )

inline

Calculate margin of error for proportion.

MoE = z_{alpha/2} * sqrt(p(1-p)/n)

Parameters

successes	Number of successes
n	Sample size
confidence	Confidence level (default: 0.95)

Returns

Margin of error

Exceptions

std::invalid_argument

If confidence level is outside (0, 1), n is 0, or successes exceeds n

Definition at line 529 of file estimation.hpp.

margin_of_error_proportion_worst_case()

double statcpp::margin_of_error_proportion_worst_case ( std::size_t  n, double  confidence = 0.95  )

inline

Calculate worst-case margin of error for proportion.

Maximum at p=0.5: MoE = z_{alpha/2} * 0.5/sqrt(n)

Parameters

n	Sample size
confidence	Confidence level (default: 0.95)

Returns

Margin of error

Exceptions

std::invalid_argument

If confidence level is outside (0, 1) or n is 0

Definition at line 560 of file estimation.hpp.

maximum() [1/2]

template<typename Iterator >

auto statcpp::maximum	(	Iterator	first,
		Iterator	last
	)

Return maximum value.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range

Returns

Maximum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 177 of file order_statistics.hpp.

maximum() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::maximum	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Return maximum value with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
proj	Projection function

Returns

Maximum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 197 of file order_statistics.hpp.

mean() [1/2]

template<typename Iterator >

double statcpp::mean	(	Iterator	first,
		Iterator	last
	)

Arithmetic mean.

Computes the arithmetic mean of elements in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Arithmetic mean

Exceptions

std::invalid_argument

If range is empty

Definition at line 112 of file basic_statistics.hpp.

mean() [2/2]

template<typename Iterator , typename Projection >

double statcpp::mean	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Arithmetic mean of projected values using a lambda expression.

Computes the arithmetic mean of the results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Arithmetic mean of projected values

Exceptions

std::invalid_argument

If range is empty

Definition at line 139 of file basic_statistics.hpp.

mean_absolute_deviation() [1/4]

template<typename Iterator >

double statcpp::mean_absolute_deviation	(	Iterator	first,
		Iterator	last
	)

Mean absolute deviation.

Computes the mean of absolute deviations from the mean. A measure of dispersion less sensitive to outliers than variance.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Mean absolute deviation

Exceptions

std::invalid_argument

If the range is empty

Definition at line 1010 of file dispersion_spread.hpp.

mean_absolute_deviation() [2/4]

template<typename Iterator >

double statcpp::mean_absolute_deviation	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Mean absolute deviation using precomputed mean.

Computes mean absolute deviation when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Mean absolute deviation

Exceptions

std::invalid_argument

If the range is empty

Definition at line 1037 of file dispersion_spread.hpp.

mean_absolute_deviation() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::mean_absolute_deviation	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Mean absolute deviation of projected values using a lambda expression.

Computes the mean absolute deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Mean absolute deviation of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 1067 of file dispersion_spread.hpp.

mean_absolute_deviation() [4/4]

template<typename Iterator , typename Projection >

double statcpp::mean_absolute_deviation	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Mean absolute deviation of projected values using precomputed mean.

Computes mean absolute deviation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Mean absolute deviation of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 1096 of file dispersion_spread.hpp.

median() [1/2]

template<typename Iterator >

double statcpp::median	(	Iterator	first,
		Iterator	last
	)

Median (accepts a sorted range)

Computes the median of a sorted range. Returns the average of the two middle values if the number of elements is even.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Median

Exceptions

std::invalid_argument

If range is empty

Definition at line 169 of file basic_statistics.hpp.

median() [2/2]

template<typename Iterator , typename Projection >

double statcpp::median	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Median of projected values using a lambda expression (projection results must be in sorted order)

Computes the median of the results after applying a projection function to each element. Assumes that projection results are sorted.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Median of projected values

Exceptions

std::invalid_argument

If range is empty

Definition at line 204 of file basic_statistics.hpp.

median_survival_time()

double statcpp::median_survival_time ( const kaplan_meier_result &  km )

inline

Calculate median survival time.

Returns the time at which survival probability reaches 50%. Returns NaN if 50% is not reached.

Parameters

km	Kaplan-Meier estimation result

Returns

Median survival time (NaN if 50% is not reached)

Definition at line 286 of file survival.hpp.

min_max_scale()

std::vector< std::vector< double > > statcpp::min_max_scale ( const std::vector< std::vector< double > > &  data )

inline

Min-Max normalization (0-1 scaling)

Scales each variable to the [0, 1] range. Data is passed with rows=observations and columns=variables.

Parameters

data	Matrix data (rows=observations, columns=variables)

Returns

Scaled data

Exceptions

std::invalid_argument

If data is empty, rows have different column counts, or any variable has zero range

Definition at line 198 of file multivariate.hpp.

minimum() [1/2]

template<typename Iterator >

auto statcpp::minimum	(	Iterator	first,
		Iterator	last
	)

Return minimum value.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range

Returns

Minimum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 128 of file order_statistics.hpp.

minimum() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::minimum	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Return minimum value with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
proj	Projection function

Returns

Minimum value

Exceptions

std::invalid_argument

If range is empty

Definition at line 148 of file order_statistics.hpp.

minkowski_distance() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::minkowski_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	p
	)

Minkowski distance (generalized Lp distance)

Computes the Minkowski distance with parameter p: d(x, y) = (sum(|x_i - y_i|^p))^(1/p)

Special cases:

• p = 1: Manhattan distance
• p = 2: Euclidean distance
• p → ∞: Chebyshev distance (max |x_i - y_i|)

Template Parameters

Iterator1	RandomAccessIterator type for first sequence
Iterator2	RandomAccessIterator type for second sequence

Parameters

first1	Beginning of first sequence
last1	End of first sequence
first2	Beginning of second sequence
last2	End of second sequence
p	The order of the Minkowski distance (must be >= 1)

Returns

Minkowski distance

Exceptions

std::invalid_argument

if sequences have different lengths or p < 1

Definition at line 401 of file distance_metrics.hpp.

minkowski_distance() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Proj1 , typename Proj2 >

double statcpp::minkowski_distance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	p,
		Proj1	proj1,
		Proj2	proj2
	)

Minkowski distance with projection.

Definition at line 437 of file distance_metrics.hpp.

mode() [1/2]

template<typename Iterator >

auto statcpp::mode	(	Iterator	first,
		Iterator	last
	)

Mode (returns the smallest value when there are multiple modes: guarantees deterministic behavior)

Returns the most frequent value in the range. When there are multiple modes, returns the smallest value.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Mode

Exceptions

std::invalid_argument

If range is empty

Definition at line 242 of file basic_statistics.hpp.

mode() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::mode	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Mode of projected values using a lambda expression.

Returns the most frequent value after applying a projection function to each element. When there are multiple modes, returns the smallest value.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Mode of projected values

Exceptions

std::invalid_argument

If range is empty

Definition at line 286 of file basic_statistics.hpp.

modes() [1/2]

template<typename Iterator >

auto statcpp::modes	(	Iterator	first,
		Iterator	last
	)		-> std::vector<typename std::iterator_traits<Iterator>::value_type>

Returns all modes (returns a vector sorted in ascending order)

Returns all most frequent values in the range. When there are multiple modes, returns all of them in ascending order as a vector.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Vector of modes (ascending order)

Exceptions

std::invalid_argument

If range is empty

Definition at line 334 of file basic_statistics.hpp.

modes() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::modes	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> std::vector<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>>

Returns all modes of projected values using a lambda expression.

Returns all most frequent values after applying a projection function to each element. When there are multiple modes, returns all of them in ascending order as a vector.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Vector of modes of projected values (ascending order)

Exceptions

std::invalid_argument

If range is empty

Definition at line 389 of file basic_statistics.hpp.

moving_average()

template<typename Iterator >

std::vector< double > statcpp::moving_average	(	Iterator	first,
		Iterator	last,
		std::size_t	window
	)

Simple moving average.

Calculates the simple moving average with the specified window size.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
window	Window size

Returns

Vector of moving averages

Exceptions

std::invalid_argument

If range is empty or window size is invalid

Definition at line 328 of file time_series.hpp.

mse()

template<typename Iterator1 , typename Iterator2 >

double statcpp::mse	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2
	)

Mean Squared Error (MSE)

Calculates the mean squared error between actual and predicted values.

Template Parameters

Iterator1	RandomAccessIterator type for actual values
Iterator2	RandomAccessIterator type for predicted values

Parameters

first1	Beginning iterator of actual values
last1	End iterator of actual values
first2	Beginning iterator of predicted values

Returns

MSE

Exceptions

std::invalid_argument

If range is empty

Definition at line 237 of file time_series.hpp.

multicollinearity_score()

double statcpp::multicollinearity_score ( const std::vector< std::vector< double > > &  X )

inline

Calculate multicollinearity score.

Score ranges from 0 to 1, with values closer to 1 indicating stronger multicollinearity. Calculated as Score = 1 - |det(R)|.

Parameters

X	Predictor matrix (n x p)

Returns

double Multicollinearity score (0: no correlation, 1: perfect multicollinearity)

Exceptions

std::invalid_argument	If there are fewer than 2 observations
std::invalid_argument	If there are fewer than 2 or more than 3 predictors

Definition at line 1098 of file linear_regression.hpp.

multiple_imputation_bootstrap()

multiple_imputation_result statcpp::multiple_imputation_bootstrap ( const std::vector< std::vector< double > > &  data, std::size_t  m = 5, unsigned int  seed = 0  )

inline

Multiple imputation (simplified Bootstrap EM method)

Performs multiple imputation combining bootstrap sampling with stochastic imputation from normal distribution. Results are pooled based on Rubin's rules.

Parameters

data	Input data (rows: observations, columns: variables)
m	Number of imputations (default: 5)
seed	Random seed (0 for random seed)

Returns

multiple_imputation_result Multiple imputation result

Exceptions

std::invalid_argument

If data is empty

Definition at line 646 of file missing_data.hpp.

multiple_imputation_pmm()

multiple_imputation_result statcpp::multiple_imputation_pmm ( const std::vector< std::vector< double > > &  data, std::size_t  m = 5, unsigned int  seed = 0  )

inline

Multiple imputation (PMM: Predictive Mean Matching)

Performs multiple imputation using Predictive Mean Matching method. Randomly selects a donor from k observations closest to the predicted value. Results are pooled based on Rubin's rules.

Parameters

data	Input data (rows: observations, columns: variables)
m	Number of imputations (default: 5)
seed	Random seed (0 for random seed)

Returns

multiple_imputation_result Multiple imputation result

Exceptions

std::invalid_argument

If data is empty

Definition at line 480 of file missing_data.hpp.

multiple_linear_regression()

multiple_regression_result statcpp::multiple_linear_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y  )

inline

Perform multiple linear regression.

Estimates multiple regression model y = b0 + b1*x1 + ... + bp*xp using least squares method. The intercept is added automatically, so X should not contain an intercept column.

Parameters

X	Predictor matrix (n x p). Each row is one observation, each column is one predictor
y	Response variable vector (n-dimensional)

Returns

multiple_regression_result Regression analysis results

Exceptions

std::invalid_argument	If data is empty
std::invalid_argument	If X and Y have different numbers of observations
std::invalid_argument	If number of predictors is greater than or equal to number of observations
std::invalid_argument	If X contains an intercept column (all 1s column)

Definition at line 523 of file linear_regression.hpp.

nbinom_cdf()

double statcpp::nbinom_cdf ( std::uint64_t  k, double  r, double  p  )

inline

Negative binomial distribution cumulative distribution function (CDF)

P(X <= k) = I_p(r, k+1) (using incomplete beta function)

Parameters

k	Upper bound of failures
r	Number of successes required
p	Probability of success

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If r <= 0 or p is outside (0, 1]

Definition at line 629 of file discrete_distributions.hpp.

nbinom_pmf()

double statcpp::nbinom_pmf ( std::uint64_t  k, double  r, double  p  )

inline

Negative binomial distribution probability mass function (PMF)

P(X = k) = C(k+r-1, k) * p^r * (1-p)^k X = Number of failures before r successes (support: k = 0, 1, 2, ...)

Parameters

k	Number of failures
r	Number of successes required (dispersion parameter, > 0, can be non-integer)
p	Probability of success

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If r <= 0 or p is outside (0, 1]

Note

About parameterization: There are multiple parameterizations for the negative binomial distribution. This implementation uses the "number of failures" form (X = number of failures before r successes).

• R's dnbinom(x, size, prob): size=r, prob=p (same, counts failures)
• Python scipy.stats.nbinom(k, n, p): n=r, p=p (same, counts failures)
• Some textbooks: "number of trials until r successes" = X + r

There is also a "mean-dispersion" parameterization:

• Mean μ = r(1-p)/p
• Variance σ² = r(1-p)/p² = μ + μ²/r This form is commonly used for modeling overdispersed data (GLM, etc.).

Definition at line 603 of file discrete_distributions.hpp.

nbinom_quantile()

std::uint64_t statcpp::nbinom_quantile ( double  prob, double  r, double  p  )

inline

Negative binomial distribution quantile function (inverse CDF)

Parameters

prob	Cumulative probability
r	Number of successes required
p	Probability of success

Returns

Smallest k such that P(X <= k) >= prob

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 651 of file discrete_distributions.hpp.

nbinom_rand() [1/2]

std::uint64_t statcpp::nbinom_rand ( double  r, double  p  )

inline

Negative binomial distribution random number generation (using default engine)

Parameters

r	Number of successes required
p	Probability of success

Returns

Generated random number

Definition at line 727 of file discrete_distributions.hpp.

nbinom_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::nbinom_rand	(	double	r,
		double	p,
		Engine &	engine
	)

Negative binomial distribution random number generation.

Generated as a Poisson-Gamma mixture.

Template Parameters

Engine

Random engine type

Parameters

r	Number of successes required
p	Probability of success
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 703 of file discrete_distributions.hpp.

nelson_aalen()

hazard_rate_result statcpp::nelson_aalen ( const std::vector< double > &  times, const std::vector< bool > &  events  )

inline

Nelson-Aalen cumulative hazard estimation.

Estimates the cumulative hazard function H(t) using the Nelson-Aalen estimator. Handles survival time data with censoring.

Note

The Nelson-Aalen estimator is a nonparametric estimator of the cumulative hazard function: H(t) = sum_{t_i <= t} d_i / n_i where d_i is the number of events at time t_i and n_i is the risk set size.

Relationship between cumulative hazard and survival function:

• S(t) = exp(-H(t)) (approximation via exponential transformation)
• Kaplan-Meier estimator directly estimates S(t) = prod(1 - d_i/n_i)
• For small event probabilities, both are approximately equal

Advantages of Nelson-Aalen estimation:

• Simpler confidence interval construction (variance estimated by sum d_i/n_i^2)
• Consistent with Cox regression baseline hazard estimation (Breslow estimator)

Parameters

times	Vector of observation times
events	Event occurrence flags (true = event occurred, false = censored)

Returns

Hazard rate estimation result

Exceptions

std::invalid_argument

If times and events have different sizes or data is empty

Definition at line 337 of file survival.hpp.

norm_cdf()

double statcpp::norm_cdf ( double  x )

inline

Standard normal CDF.

Computes the cumulative distribution function Phi(x) of the standard normal distribution.

Parameters

x

Argument

Returns

Phi(x) = P(Z <= x) where Z ~ N(0, 1)

Definition at line 394 of file special_functions.hpp.

norm_quantile()

double statcpp::norm_quantile ( double  p )

inline

Standard normal quantile function.

Computes the quantile function Phi^{-1}(p) of the standard normal distribution.

Parameters

p	Probability (must be in (0, 1))

Returns

x such that Phi(x) = p

Note

Reference: https://home.online.no/~pjacklam/notes/invnorm/

Rational approximation by Acklam's algorithm

Definition at line 410 of file special_functions.hpp.

normal_cdf()

double statcpp::normal_cdf ( double  x, double  mu = 0.0, double  sigma = 1.0  )

inline

Normal distribution cumulative distribution function (CDF)

F(x) = Phi((x - mu) / sigma)

Parameters

x	Random variable value
mu	Mean (default: 0.0)
sigma	Standard deviation (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 159 of file continuous_distributions.hpp.

normal_pdf()

double statcpp::normal_pdf ( double  x, double  mu = 0.0, double  sigma = 1.0  )

inline

Normal distribution probability density function (PDF)

f(x) = (1 / (sigma * sqrt(2 * pi))) * exp(-(x-mu)^2/(2*sigma^2))

Parameters

x	Random variable value
mu	Mean (default: 0.0)
sigma	Standard deviation (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 139 of file continuous_distributions.hpp.

normal_quantile()

double statcpp::normal_quantile ( double  p, double  mu = 0.0, double  sigma = 1.0  )

inline

Normal distribution quantile function (inverse CDF, percent point function)

Returns the quantile (percentile value) corresponding to probability p. Q(p) = mu + sigma * Phi^(-1)(p)

where Phi^(-1)(p) is the inverse cumulative distribution function of the standard normal distribution (probit function). Example: Q(0.975) is approximately mu + 1.96*sigma (upper bound of 95% confidence interval)

Parameters

p	Probability (0 < p < 1)
mu	Mean (default: 0.0)
sigma	Standard deviation (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If sigma <= 0 or p is outside (0, 1)

Note

Boundary value handling: returns -infinity for p = 0, +infinity for p = 1.

Definition at line 185 of file continuous_distributions.hpp.

normal_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::normal_rand	(	double	mu,
		double	sigma,
		Engine &	engine
	)

Normal distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

mu	Mean
sigma	Standard deviation
engine	Random engine

Returns

Random number following normal distribution

Exceptions

std::invalid_argument

If sigma <= 0

Definition at line 209 of file continuous_distributions.hpp.

normal_rand() [2/2]

double statcpp::normal_rand ( double  mu = 0.0, double  sigma = 1.0  )

inline

Normal distribution random number generation (using default engine)

Parameters

mu	Mean (default: 0.0)
sigma	Standard deviation (default: 1.0)

Returns

Random number following normal distribution

Definition at line 225 of file continuous_distributions.hpp.

number_needed_to_treat()

double statcpp::number_needed_to_treat ( const std::vector< std::vector< std::size_t > > &  table )

inline

Calculate Number Needed to Treat (NNT)

Calculated as the reciprocal of the risk difference. Represents the number of patients that need to be treated to prevent one outcome.

Parameters

table

2x2 contingency table

Returns

Number needed to treat

Exceptions

std::invalid_argument

If risk difference is zero

Definition at line 331 of file categorical.hpp.

odds_ratio() [1/3]

odds_ratio_result statcpp::odds_ratio ( const std::vector< std::vector< std::size_t > > &  table )

inline

Calculate odds ratio from a 2x2 contingency table.

Calculates the odds ratio and its confidence interval. Odds ratio = (a * d) / (b * c)

Parameters

table

2x2 contingency table in the form [[a, b], [c, d]] a: Exposed and diseased b: Exposed and not diseased c: Not exposed and diseased d: Not exposed and not diseased

Returns

Odds ratio calculation result

Exceptions

std::invalid_argument

If table is not 2x2 or if cell count is zero

Note

Currently throws an exception when any cell count is zero. A future enhancement may add an optional Gart-Zweifel continuity correction (+0.5 to all cells) to handle zero-cell tables.

Definition at line 115 of file categorical.hpp.

odds_ratio() [2/3]

double statcpp::odds_ratio ( double  a, double  b, double  c, double  d  )

inline

Odds ratio.

Calculates the odds ratio from a 2x2 contingency table.

Parameters

a	Cell (1,1) frequency (exposed, disease present)
b	Cell (1,2) frequency (exposed, disease absent)
c	Cell (2,1) frequency (unexposed, disease present)
d	Cell (2,2) frequency (unexposed, disease absent)

Returns

Odds ratio

Exceptions

std::invalid_argument

If b or c is zero

Definition at line 381 of file effect_size.hpp.

odds_ratio() [3/3]

odds_ratio_result statcpp::odds_ratio ( std::size_t  a, std::size_t  b, std::size_t  c, std::size_t  d  )

inline

Calculate odds ratio from a 2x2 contingency table (specifying cell values directly)

Parameters

a	Exposed and diseased
b	Exposed and not diseased
c	Not exposed and diseased
d	Not exposed and not diseased

Returns

Odds ratio calculation result

Exceptions

std::invalid_argument

If cell count is zero

Definition at line 152 of file categorical.hpp.

odds_ratios()

std::vector< double > statcpp::odds_ratios ( const glm_result &  model )

inline

Calculate odds ratios.

Calculates odds ratios from logistic regression model coefficients.

Parameters

model

Fitted logistic regression model

Returns

Vector of odds ratios for each predictor (excluding intercept)

Exceptions

std::invalid_argument

If model is not logistic regression

Definition at line 731 of file glm.hpp.

odds_ratios_ci()

std::vector< std::pair< double, double > > statcpp::odds_ratios_ci ( const glm_result &  model, double  confidence = 0.95  )

inline

Confidence intervals for odds ratios.

Calculates confidence intervals for odds ratios from a logistic regression model.

Parameters

model	Fitted logistic regression model
confidence	Confidence level (default: 0.95)

Returns

Vector of (lower, upper) pairs for each predictor's odds ratio

Exceptions

std::invalid_argument

If model is not logistic regression or confidence level is outside (0,1)

Definition at line 754 of file glm.hpp.

omega_squared() [1/2]

double statcpp::omega_squared ( const one_way_anova_result &  result )

inline

Calculate Omega-squared for one-way ANOVA.

A less biased effect size estimate compared to Eta-squared. Suitable for estimating population effect size.

Parameters

result

Result from one-way ANOVA

Returns

double Omega-squared value

Definition at line 899 of file anova.hpp.

omega_squared() [2/2]

double statcpp::omega_squared ( double  ss_effect, double  ss_total, double  ms_error, double  df_effect  )

inline

Omega-squared.

A less biased estimate of effect size than eta-squared.

Parameters

ss_effect	Sum of squares for effect
ss_total	Total sum of squares
ms_error	Mean square error
df_effect	Degrees of freedom for effect

Returns

Omega-squared

Exceptions

std::invalid_argument

If ss_total is not positive

Definition at line 333 of file effect_size.hpp.

one_hot_encode()

template<typename T >

std::vector< std::vector< double > > statcpp::one_hot_encode

(

const std::vector< T > &

data

)

One-hot encoding.

Template Parameters

T

Data type

Parameters

data	Data vector

Returns

One-hot encoded 2-dimensional vector

Definition at line 1001 of file data_wrangling.hpp.

one_way_ancova()

ancova_result statcpp::one_way_ancova ( const std::vector< std::vector< std::pair< double, double > > > &  groups )

inline

Perform one-way analysis of covariance.

Tests differences in group means while controlling for the effect of a covariate. Each observation is specified as a pair of dependent variable (y) and covariate (x).

Parameters

groups

Data for each group. groups[i] is a vector of (y, x) pairs for group i

Returns

ancova_result Results of the analysis of covariance

Exceptions

std::invalid_argument	If number of groups is less than 2
std::invalid_argument	If an empty group exists
std::invalid_argument	If number of observations is insufficient

Definition at line 688 of file anova.hpp.

one_way_anova()

one_way_anova_result statcpp::one_way_anova ( const std::vector< std::vector< double > > &  groups )

inline

Perform one-way analysis of variance.

Tests whether there are significant differences in means among multiple groups. Uses F-test to compare between-group and within-group variation.

Parameters

groups

Vector of vectors containing data for each group

Returns

one_way_anova_result Results of the analysis of variance

Exceptions

std::invalid_argument	If number of groups is less than 2
std::invalid_argument	If an empty group exists
std::invalid_argument	If total number of observations is less than or equal to number of groups

Definition at line 125 of file anova.hpp.

overdispersion_test()

double statcpp::overdispersion_test ( const glm_result &  model, const std::vector< std::vector< double > > &  X, const std::vector< double > &  y  )

inline

Overdispersion test (for Poisson regression)

Calculates the overdispersion parameter for a Poisson regression model. Values greater than 1 suggest the presence of overdispersion.

Parameters

model	Fitted Poisson regression model
X	Predictor matrix
y	Response variable vector

Returns

Overdispersion parameter (Pearson chi-square statistic / residual degrees of freedom)

Exceptions

std::invalid_argument

If model is not Poisson

Definition at line 946 of file glm.hpp.

pacf()

template<typename Iterator >

std::vector< double > statcpp::pacf	(	Iterator	first,
		Iterator	last,
		std::size_t	max_lag
	)

Calculate partial autocorrelation function (PACF) (Durbin-Levinson algorithm)

Calculates PACF using the Durbin-Levinson algorithm.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
max_lag	Maximum lag

Returns

Vector of partial autocorrelation coefficients

Exceptions

std::invalid_argument

If range is empty

Definition at line 134 of file time_series.hpp.

partial_eta_squared()

double statcpp::partial_eta_squared ( double  f, double  df1, double  df2  )

inline

Calculate partial eta-squared from F-test.

Parameters

f	F-statistic
df1	Numerator degrees of freedom
df2	Denominator degrees of freedom

Returns

Partial eta-squared

Definition at line 312 of file effect_size.hpp.

partial_eta_squared_a()

double statcpp::partial_eta_squared_a ( const two_way_anova_result &  result )

inline

Calculate Partial eta-squared for factor A in two-way ANOVA.

Indicates the proportion of factor A effect relative to the sum of factor A effect and error.

Parameters

result

Result from two-way ANOVA

Returns

double Partial eta-squared value for factor A

Definition at line 845 of file anova.hpp.

partial_eta_squared_b()

double statcpp::partial_eta_squared_b ( const two_way_anova_result &  result )

inline

Calculate Partial eta-squared for factor B in two-way ANOVA.

Indicates the proportion of factor B effect relative to the sum of factor B effect and error.

Parameters

result

Result from two-way ANOVA

Returns

double Partial eta-squared value for factor B

Definition at line 863 of file anova.hpp.

partial_eta_squared_interaction()

double statcpp::partial_eta_squared_interaction ( const two_way_anova_result &  result )

inline

Calculate Partial eta-squared for interaction in two-way ANOVA.

Indicates the proportion of interaction effect relative to the sum of interaction effect and error.

Parameters

result

Result from two-way ANOVA

Returns

double Partial eta-squared value for interaction

Definition at line 881 of file anova.hpp.

pca()

pca_result statcpp::pca ( const std::vector< std::vector< double > > &  data, std::size_t  n_components  )

inline

Principal Component Analysis.

Finds principal components through eigenvalue decomposition of the covariance matrix. Uses deflation method to compute multiple principal components.

Parameters

data	Matrix data (rows=observations, columns=variables)
n_components	Number of principal components to extract

Returns

PCA result

Exceptions

std::invalid_argument

If data is empty or rows have different column counts

Note

This implementation uses the deflation method to extract multiple principal components. The deflation method may accumulate numerical errors when extracting many components. For high-dimensional data or when many components are needed, consider verifying results against a full eigendecomposition approach.

Definition at line 325 of file multivariate.hpp.

pca_transform()

std::vector< std::vector< double > > statcpp::pca_transform ( const std::vector< std::vector< double > > &  data, const pca_result &  pca  )

inline

Project data onto principal component space.

Transforms data to principal component space using PCA results.

Parameters

data	Matrix data (rows=observations, columns=variables)
pca	PCA result

Returns

Data projected onto principal component space (n x n_components)

Exceptions

std::invalid_argument

If data is empty, PCA components are empty, or dimensions don't match

Definition at line 385 of file multivariate.hpp.

pearson_correlation() [1/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::pearson_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Pearson correlation coefficient.

Computes the Pearson product-moment correlation coefficient of two variables. r = Cov(X, Y) / (sigma_x * sigma_y) Values range from -1 to 1, where 1 indicates perfect positive correlation and -1 indicates perfect negative correlation.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Pearson correlation coefficient (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, number of elements is less than 2, or variance of either variable is zero

Definition at line 376 of file correlation_covariance.hpp.

pearson_correlation() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::pearson_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	mean_x,
		double	mean_y
	)

Pearson correlation coefficient with precomputed means.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
mean_x	Mean of the first data
mean_y	Mean of the second data

Returns

Pearson correlation coefficient (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, number of elements is less than 2, or variance of either variable is zero

Definition at line 432 of file correlation_covariance.hpp.

pearson_correlation() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::pearson_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Pearson correlation coefficient (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Pearson correlation coefficient (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, number of elements is less than 2, or variance of either variable is zero

Definition at line 488 of file correlation_covariance.hpp.

percentile() [1/2]

template<typename Iterator >

double statcpp::percentile	(	Iterator	first,
		Iterator	last,
		double	p
	)

Return percentile.

Calculates specified percentile from sorted range.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of sorted range
last	End of sorted range
p	Percentile as proportion 0.0-1.0 (e.g., 90th percentile -> p = 0.9)

Returns

Percentile value

Exceptions

std::invalid_argument

If range is empty or p is out of range

Definition at line 285 of file order_statistics.hpp.

percentile() [2/2]

template<typename Iterator , typename Projection >

double statcpp::percentile	(	Iterator	first,
		Iterator	last,
		double	p,
		Projection	proj
	)

Return percentile with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of sorted range
last	End of sorted range
p	Percentile as proportion 0.0-1.0
proj	Projection function

Returns

Percentile value

Exceptions

std::invalid_argument

If range is empty or p is out of range

Definition at line 310 of file order_statistics.hpp.

permutation_test_correlation()

template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>

permutation_result statcpp::permutation_test_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		std::size_t	n_permutations = 10000,
		Engine &	engine = get_random_engine()
	)

Perform permutation test for correlation.

Performs a permutation test for Pearson correlation coefficient between two variables. Generates the null distribution by shuffling one variable. The null hypothesis is "there is no correlation between the two variables (correlation is 0)". Computes two-sided p-value.

Note

P-value calculation uses the inclusive method: p = (count of permutation statistics as extreme or more extreme than observed + 1) / (n_permutations + 1) This method prevents p-values from being zero and provides more accurate estimation (Phipson & Smyth, 2010).

Template Parameters

Iterator1	Iterator type for first variable
Iterator2	Iterator type for second variable
Engine	Random engine type (default: default_random_engine)

Parameters

first1	Beginning iterator of first variable
last1	End iterator of first variable
first2	Beginning iterator of second variable
last2	End iterator of second variable
n_permutations	Number of permutations (default: 10000)
engine	Reference to random engine

Returns

permutation_result structure containing permutation test results

Exceptions

std::invalid_argument	If the two variables have different lengths
std::invalid_argument	If number of data pairs is less than 3

Definition at line 625 of file resampling.hpp.

permutation_test_paired()

template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>

permutation_result statcpp::permutation_test_paired	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		std::size_t	n_permutations = 10000,
		Engine &	engine = get_random_engine()
	)

Perform paired permutation test.

Performs a permutation test for differences between two paired samples. Generates the null distribution by randomly flipping the signs of differences. The null hypothesis is "the mean of differences is zero". Computes two-sided p-value.

P-value calculation uses the inclusive method: p = (count(|T*| >= |T_obs|) + 1) / (n_permutations + 1)

Template Parameters

Iterator1	Iterator type for first sample
Iterator2	Iterator type for second sample
Engine	Random engine type (default: default_random_engine)

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
n_permutations	Number of permutations (default: 10000)
engine	Reference to random engine

Returns

permutation_result structure containing permutation test results

Exceptions

std::invalid_argument	If the two samples have different lengths
std::invalid_argument	If samples are empty

Definition at line 538 of file resampling.hpp.

permutation_test_two_sample()

template<typename Iterator1 , typename Iterator2 , typename Engine = default_random_engine>

permutation_result statcpp::permutation_test_two_sample	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		std::size_t	n_permutations = 10000,
		Engine &	engine = get_random_engine()
	)

Perform two-sample permutation test (test of difference in means)

Performs a permutation test for the difference in means between two independent samples. The null hypothesis is "the two group means are equal". Computes two-sided p-value.

P-value calculation uses the inclusive method: p = (count(|T*| >= |T_obs|) + 1) / (n_permutations + 1) This includes the observed data itself as part of the null distribution, preventing p-values from being zero (Phipson & Smyth, 2010).

Template Parameters

Iterator1	Iterator type for first sample
Iterator2	Iterator type for second sample
Engine	Random engine type (default: default_random_engine)

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
n_permutations	Number of permutations (default: 10000)
engine	Reference to random engine

Returns

permutation_result structure containing permutation test results

Exceptions

std::invalid_argument

If either sample is empty

Definition at line 457 of file resampling.hpp.

poisson_cdf()

double statcpp::poisson_cdf ( std::uint64_t  k, double  lambda  )

inline

Poisson distribution cumulative distribution function (CDF)

Calculates P(X <= k).

Parameters

k	Upper bound of number of event occurrences
lambda	Mean rate

Returns

Cumulative probability P(X <= k)

Exceptions

std::invalid_argument

If lambda is negative

Definition at line 228 of file discrete_distributions.hpp.

poisson_pmf()

double statcpp::poisson_pmf ( std::uint64_t  k, double  lambda  )

inline

Poisson distribution probability mass function (PMF)

P(X = k) = (lambda^k * e^(-lambda)) / k!

Parameters

k	Number of event occurrences
lambda	Mean rate (lambda > 0)

Returns

Probability P(X = k)

Exceptions

std::invalid_argument

If lambda is negative

Definition at line 207 of file discrete_distributions.hpp.

poisson_quantile()

std::uint64_t statcpp::poisson_quantile ( double  p, double  lambda  )

inline

Poisson distribution quantile function.

Parameters

p	Probability value
lambda	Mean rate

Returns

Quantile

Exceptions

std::invalid_argument

If lambda is negative or p is in an invalid range

Definition at line 247 of file discrete_distributions.hpp.

poisson_rand() [1/2]

std::uint64_t statcpp::poisson_rand ( double  lambda )

inline

Poisson distribution random number generation (using default engine)

Parameters

lambda

Mean rate

Returns

Generated random number

Definition at line 306 of file discrete_distributions.hpp.

poisson_rand() [2/2]

template<typename Engine = default_random_engine>

std::uint64_t statcpp::poisson_rand	(	double	lambda,
		Engine &	engine
	)

Poisson distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

lambda	Mean rate
engine	Random engine

Returns

Generated random number

Exceptions

std::invalid_argument

If lambda is negative

Definition at line 291 of file discrete_distributions.hpp.

poisson_regression()

glm_result statcpp::poisson_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, std::size_t  max_iter = 100, double  tol = 1e-8  )

inline

Poisson regression.

Fits a generalized linear model using Poisson distribution and log link function. Used for regression analysis of count data.

Parameters

X	Predictor matrix (intercept is added automatically)
y	Response variable vector (non-negative count data)
max_iter	Maximum number of iterations (default: 100)
tol	Convergence tolerance (default: 1e-8)

Returns

GLM estimation results

Exceptions

std::invalid_argument

If y is negative or X contains an intercept column

Definition at line 794 of file glm.hpp.

population_covariance() [1/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::population_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Population covariance.

Computes the population covariance of two variables. Cov(X, Y) = E[(X - mu_x)(Y - mu_y)] = (1/n) * sum((x_i - x_bar)(y_i - y_bar))

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Population covariance

Exceptions

std::invalid_argument

If range is empty or lengths differ

Definition at line 46 of file correlation_covariance.hpp.

population_covariance() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::population_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	mean_x,
		double	mean_y
	)

Population covariance with precomputed means.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
mean_x	Mean of the first data
mean_y	Mean of the second data

Returns

Population covariance

Exceptions

std::invalid_argument

If range is empty or lengths differ

Definition at line 87 of file correlation_covariance.hpp.

population_covariance() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::population_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Population covariance (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Population covariance

Exceptions

std::invalid_argument

If range is empty or lengths differ

Definition at line 128 of file correlation_covariance.hpp.

population_kurtosis() [1/4]

template<typename Iterator >

double statcpp::population_kurtosis	(	Iterator	first,
		Iterator	last
	)

Calculate population kurtosis (Excess Kurtosis)

Calculates the kurtosis of a population. An indicator of tail heaviness.

Formula: g2 = E[(X - mu)^4] / sigma^4 - 3 Subtracts 3 so that normal distribution kurtosis is 0 (excess kurtosis)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Population kurtosis value (positive = heavy tails, negative = light tails)

Exceptions

std::invalid_argument

If range is empty or variance is zero

Note

The kurtosis (excess kurtosis) of a normal distribution is 0

Definition at line 375 of file shape_of_distribution.hpp.

population_kurtosis() [2/4]

template<typename Iterator >

double statcpp::population_kurtosis	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate population kurtosis with precomputed mean.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Population kurtosis value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 413 of file shape_of_distribution.hpp.

population_kurtosis() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::population_kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate population kurtosis with projection.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Population kurtosis value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 454 of file shape_of_distribution.hpp.

population_kurtosis() [4/4]

template<typename Iterator , typename Projection >

double statcpp::population_kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate population kurtosis with projection and precomputed mean.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Population kurtosis value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 494 of file shape_of_distribution.hpp.

population_skewness() [1/4]

template<typename Iterator >

double statcpp::population_skewness	(	Iterator	first,
		Iterator	last
	)

Calculate population skewness (Fisher's definition)

Calculates the skewness of a population. An indicator of distribution asymmetry.

Formula: g1 = E[(X - mu)^3] / sigma^3

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Population skewness value (positive = right-skewed, negative = left-skewed)

Exceptions

std::invalid_argument

If range is empty or variance is zero

Note

The skewness of a normal distribution is 0

Definition at line 42 of file shape_of_distribution.hpp.

population_skewness() [2/4]

template<typename Iterator >

double statcpp::population_skewness	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate population skewness with precomputed mean.

Use when the mean has already been calculated. Improves computational efficiency.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Population skewness value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 81 of file shape_of_distribution.hpp.

population_skewness() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::population_skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate population skewness with projection.

Uses a projection function to extract specific values from the data to calculate skewness.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Population skewness value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 123 of file shape_of_distribution.hpp.

population_skewness() [4/4]

template<typename Iterator , typename Projection >

double statcpp::population_skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate population skewness with projection and precomputed mean.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Population skewness value

Exceptions

std::invalid_argument

If range is empty or variance is zero

Definition at line 162 of file shape_of_distribution.hpp.

population_stddev() [1/4]

template<typename Iterator >

double statcpp::population_stddev	(	Iterator	first,
		Iterator	last
	)

Population standard deviation.

Computes the population standard deviation (square root of variance divided by N).

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Population standard deviation

Exceptions

std::invalid_argument

If the range is empty

Definition at line 588 of file dispersion_spread.hpp.

population_stddev() [2/4]

template<typename Iterator >

double statcpp::population_stddev	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Population standard deviation using precomputed mean.

Computes population standard deviation when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Population standard deviation

Exceptions

std::invalid_argument

If the range is empty

Definition at line 606 of file dispersion_spread.hpp.

population_stddev() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::population_stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Population standard deviation of projected values using a lambda expression.

Computes the population standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Population standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 628 of file dispersion_spread.hpp.

population_stddev() [4/4]

template<typename Iterator , typename Projection >

double statcpp::population_stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Population standard deviation of projected values using precomputed mean.

Computes population standard deviation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Population standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 648 of file dispersion_spread.hpp.

population_variance() [1/4]

template<typename Iterator >

double statcpp::population_variance	(	Iterator	first,
		Iterator	last
	)

Population variance.

Computes the population variance (divide by N).

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Population variance

Exceptions

std::invalid_argument

If the range is empty

Definition at line 258 of file dispersion_spread.hpp.

population_variance() [2/4]

template<typename Iterator >

double statcpp::population_variance	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Population variance using precomputed mean.

Computes population variance when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Population variance

Exceptions

std::invalid_argument

If the range is empty

Definition at line 276 of file dispersion_spread.hpp.

population_variance() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::population_variance	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Population variance of projected values using a lambda expression.

Computes the population variance of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Population variance of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 298 of file dispersion_spread.hpp.

population_variance() [4/4]

template<typename Iterator , typename Projection >

double statcpp::population_variance	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Population variance of projected values using precomputed mean.

Computes population variance using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Population variance of projected values

Exceptions

std::invalid_argument

If the range is empty

Definition at line 318 of file dispersion_spread.hpp.

power_analysis_t_one_sample() [1/2]

power_result statcpp::power_analysis_t_one_sample ( double  effect_size, std::size_t  n, double  alpha, alternative_hypothesis  alt  )

inline

Power analysis for one-sample t-test (enum overload, returning struct)

Parameters

effect_size	Effect size
n	Sample size
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Power analysis result

Definition at line 615 of file power_analysis.hpp.

power_analysis_t_one_sample() [2/2]

power_result statcpp::power_analysis_t_one_sample ( double  effect_size, std::size_t  n, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Power analysis for one-sample t-test (calculate power)

Parameters

effect_size	Effect size
n	Sample size
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Power analysis result

Definition at line 469 of file power_analysis.hpp.

power_analysis_t_one_sample_n() [1/2]

power_result statcpp::power_analysis_t_one_sample_n ( double  effect_size, double  power, double  alpha, alternative_hypothesis  alt  )

inline

Power analysis for one-sample t-test, sample size (enum overload, returning struct)

Parameters

effect_size	Effect size
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Power analysis result

Definition at line 631 of file power_analysis.hpp.

power_analysis_t_one_sample_n() [2/2]

power_result statcpp::power_analysis_t_one_sample_n ( double  effect_size, double  power = 0.80, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Power analysis for one-sample t-test (calculate sample size)

Parameters

effect_size	Effect size
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Power analysis result

Definition at line 490 of file power_analysis.hpp.

power_iteration()

std::pair< double, std::vector< double > > statcpp::power_iteration ( const std::vector< std::vector< double > > &  matrix, std::size_t  max_iter = 1000, double  tol = 1e-10  )

inline

Find largest eigenvalue and eigenvector using power iteration.

Finds the largest eigenvalue and corresponding eigenvector of a matrix through iterative computation.

Parameters

matrix	Symmetric matrix
max_iter	Maximum number of iterations (default: 1000)
tol	Convergence threshold (default: 1e-10)

Returns

Pair of (eigenvalue, eigenvector)

Definition at line 259 of file multivariate.hpp.

power_prop_test() [1/2]

double statcpp::power_prop_test ( double  p1, double  p2, std::size_t  n, double  alpha, alternative_hypothesis  alt  )

inline

Calculate power for two-sample proportion test (enum overload)

Parameters

p1	Proportion of group 1
p2	Proportion of group 2
n	Sample size per group
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Statistical power (0.0 to 1.0)

Definition at line 582 of file power_analysis.hpp.

power_prop_test() [2/2]

double statcpp::power_prop_test ( double  p1, double  p2, std::size_t  n, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Calculate power for two-sample proportion test.

Parameters

p1	Proportion of group 1
p2	Proportion of group 2
n	Sample size per group
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Statistical power (0.0 to 1.0)

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 355 of file power_analysis.hpp.

power_t_test_one_sample() [1/2]

double statcpp::power_t_test_one_sample ( double  effect_size, std::size_t  n, double  alpha, alternative_hypothesis  alt  )

inline

Calculate power for one-sample t-test (enum overload)

Parameters

effect_size	Effect size (Cohen's d)
n	Sample size
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Statistical power (0.0 to 1.0)

Definition at line 515 of file power_analysis.hpp.

power_t_test_one_sample() [2/2]

double statcpp::power_t_test_one_sample ( double  effect_size, std::size_t  n, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Calculate power for one-sample t-test.

Parameters

effect_size	Effect size (Cohen's d)
n	Sample size
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis: "two.sided", "greater", "less" (default: "two.sided")

Returns

Statistical power (0.0 to 1.0)

Exceptions

std::invalid_argument

If parameters are invalid

Note

This function uses normal distribution approximation. Strictly speaking, the noncentral t-distribution should be used, but for large sample sizes (n > 30 approximately), sufficient accuracy is obtained. For small samples, power may be slightly overestimated.

Definition at line 156 of file power_analysis.hpp.

power_t_test_two_sample() [1/2]

double statcpp::power_t_test_two_sample ( double  effect_size, std::size_t  n1, std::size_t  n2, double  alpha, alternative_hypothesis  alt  )

inline

Calculate power for two-sample t-test (enum overload)

Parameters

effect_size	Effect size (Cohen's d)
n1	Sample size of group 1
n2	Sample size of group 2
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Statistical power (0.0 to 1.0)

Definition at line 548 of file power_analysis.hpp.

power_t_test_two_sample() [2/2]

double statcpp::power_t_test_two_sample ( double  effect_size, std::size_t  n1, std::size_t  n2, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Calculate power for two-sample t-test.

Parameters

effect_size	Effect size (Cohen's d)
n1	Sample size of group 1
n2	Sample size of group 2
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Statistical power (0.0 to 1.0)

Exceptions

std::invalid_argument

If parameters are invalid

Note

This function uses normal distribution approximation. Strictly speaking, the noncentral t-distribution should be used, but for large total sample sizes (n1 + n2 > 60 approximately), sufficient accuracy is obtained. For small samples, power may be slightly overestimated.

Definition at line 255 of file power_analysis.hpp.

predict() [1/2]

double statcpp::predict ( const multiple_regression_result &  model, const std::vector< double > &  x  )

inline

Make prediction using multiple regression model.

Parameters

model	Multiple regression analysis results
x	Predictor variable vector (do not include intercept)

Returns

double Predicted value

Exceptions

std::invalid_argument

If x dimension doesn't match model's number of predictors

Definition at line 662 of file linear_regression.hpp.

predict() [2/2]

double statcpp::predict ( const simple_regression_result &  model, double  x  )

inline

Make prediction using simple regression model.

Parameters

model	Simple regression analysis results
x	Predictor variable value

Returns

double Predicted value

Definition at line 649 of file linear_regression.hpp.

predict_count()

double statcpp::predict_count ( const glm_result &  model, const std::vector< double > &  x  )

inline

Expected count prediction with Poisson regression.

Uses a fitted Poisson regression model to predict expected counts for new data points.

Parameters

model	Fitted GLM model (Poisson distribution)
x	Predictor variable vector

Returns

Predicted expected count

Exceptions

std::invalid_argument

If model is not Poisson or x dimension doesn't match

Definition at line 824 of file glm.hpp.

predict_probability()

double statcpp::predict_probability ( const glm_result &  model, const std::vector< double > &  x  )

inline

Probability prediction with logistic regression.

Uses a fitted logistic regression model to predict probabilities for new data points.

Parameters

model	Fitted GLM model (binomial distribution)
x	Predictor variable vector

Returns

Predicted probability (range 0 to 1)

Exceptions

std::invalid_argument

If model is not binomial or x dimension doesn't match

Definition at line 705 of file glm.hpp.

prediction_interval_simple()

template<typename IteratorX >

prediction_interval statcpp::prediction_interval_simple	(	const simple_regression_result &	model,
		IteratorX	x_first,
		IteratorX	x_last,
		double	x_new,
		double	confidence = 0.95
	)

Calculate prediction interval for simple regression model.

Calculates the prediction interval for a new observation. The prediction interval shows the probability that a future individual observation falls within this interval.

Template Parameters

IteratorX

Iterator type for predictor variable

Parameters

model	Simple regression analysis results
x_first	Beginning iterator for original predictor variable data
x_last	Ending iterator for original predictor variable data
x_new	x value of the point to predict
confidence	Confidence level (default: 0.95)

Returns

prediction_interval Predicted value and prediction interval

Exceptions

std::invalid_argument

If confidence is outside (0, 1) range

Definition at line 695 of file linear_regression.hpp.

press_statistic()

template<typename IteratorX , typename IteratorY >

double statcpp::press_statistic	(	IteratorX	x_first,
		IteratorX	x_last,
		IteratorY	y_first,
		IteratorY	y_last,
		const simple_regression_result &	model
	)

Calculate PRESS statistic.

Calculates the Prediction Sum of Squares (prediction residual sum of squares). Used for efficient computation of leave-one-out cross-validation.

Template Parameters

IteratorX	Iterator type for predictor variable
IteratorY	Iterator type for response variable

Parameters

x_first	Beginning iterator for predictor variable
x_last	Ending iterator for predictor variable
y_first	Beginning iterator for response variable
y_last	Ending iterator for response variable
model	Simple regression model

Returns

PRESS statistic

Exceptions

std::invalid_argument

If x and y have different lengths

Definition at line 183 of file model_selection.hpp.

pseudo_r_squared_mcfadden()

double statcpp::pseudo_r_squared_mcfadden ( const glm_result &  model )

inline

McFadden's pseudo R-squared.

Calculates McFadden's pseudo R-squared. Defined as 1 - (LL_model / LL_null).

Parameters

model

Fitted GLM model

Returns

McFadden's pseudo R-squared

Definition at line 977 of file glm.hpp.

pseudo_r_squared_nagelkerke()

double statcpp::pseudo_r_squared_nagelkerke ( const glm_result &  model, const std::vector< double > &  y, std::size_t  n  )

inline

Nagelkerke's pseudo R-squared.

Calculates Nagelkerke's pseudo R-squared. Cox-Snell pseudo R-squared adjusted to have a maximum value of 1.

Uses the relationship: deviance = -2 * (LL_model - LL_saturated), so LL_null = LL_saturated - null_deviance / 2. For binomial (0/1 responses) and Poisson, the saturated model log-likelihood is computed explicitly.

Parameters

model	Fitted GLM model
y	Response variable vector (needed to compute saturated LL for non-Gaussian)
n	Sample size

Returns

Nagelkerke's pseudo R-squared

Definition at line 999 of file glm.hpp.

quartiles() [1/2]

template<typename Iterator >

quartile_result statcpp::quartiles	(	Iterator	first,
		Iterator	last
	)

Return quartiles.

Calculates quartiles (Q1, Q2, Q3) from sorted range.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of sorted range
last	End of sorted range

Returns

Quartiles

Exceptions

std::invalid_argument

If range is empty

Note

Equivalent to R's type=7 (default) or Excel's QUARTILE.INC.

Definition at line 230 of file order_statistics.hpp.

quartiles() [2/2]

template<typename Iterator , typename Projection >

quartile_result statcpp::quartiles	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Return quartiles with projection.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning of sorted range
last	End of sorted range
proj	Projection function

Returns

Quartiles

Exceptions

std::invalid_argument

If range is empty

Definition at line 255 of file order_statistics.hpp.

r_squared()

template<typename IteratorY , typename IteratorPred >

double statcpp::r_squared	(	IteratorY	y_first,
		IteratorY	y_last,
		IteratorPred	pred_first,
		IteratorPred	pred_last
	)

Calculate coefficient of determination from observed and predicted values.

Calculated as R^2 = 1 - SS_residual / SS_total.

Template Parameters

IteratorY	Iterator type for observed values
IteratorPred	Iterator type for predicted values

Parameters

y_first	Beginning iterator for observed values
y_last	Ending iterator for observed values
pred_first	Beginning iterator for predicted values
pred_last	Ending iterator for predicted values

Returns

double Coefficient of determination R^2

Exceptions

std::invalid_argument	If y and predictions have different lengths
std::invalid_argument	If there are fewer than 2 observations

Definition at line 1125 of file linear_regression.hpp.

r_to_d()

double statcpp::r_to_d ( double  r )

inline

Convert correlation coefficient to Cohen's d.

Parameters

r	Correlation coefficient

Returns

Cohen's d

Exceptions

std::invalid_argument

If |r| >= 1

Definition at line 273 of file effect_size.hpp.

randomize_seed()

void statcpp::randomize_seed ( )

inline

Randomly reset the random engine seed.

Re-initializes the global random engine seed with a value obtained from a random device. Use this when unpredictable random sequences are needed.

Definition at line 56 of file random_engine.hpp.

range() [1/2]

template<typename Iterator >

double statcpp::range	(	Iterator	first,
		Iterator	last
	)

Range (maximum - minimum)

Computes the difference between the maximum and minimum values in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Range (maximum - minimum)

Exceptions

std::invalid_argument

If the range is empty

Definition at line 50 of file dispersion_spread.hpp.

range() [2/2]

template<typename Iterator , typename Projection >

double statcpp::range	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Range of projected values using a lambda expression.

Computes the range of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Range of projected values (maximum - minimum)

Exceptions

std::invalid_argument

If the range is empty

Definition at line 73 of file dispersion_spread.hpp.

rank_transform()

std::vector< double > statcpp::rank_transform ( const std::vector< double > &  data )

inline

Rank transformation.

Uses average rank for ties

Parameters

data	Data vector

Returns

Vector of ranks

Definition at line 415 of file data_wrangling.hpp.

relative_error()

double statcpp::relative_error ( double  x, double  x_ref  )

inline

Compute the relative error between two values.

relative_error = |x - x_ref| / max(|x_ref|, eps)

Parameters

x	Computed value
x_ref	Reference value

Returns

Relative error

Definition at line 229 of file numerical_utils.hpp.

relative_frequency() [1/2]

template<typename Iterator >

auto statcpp::relative_frequency	(	Iterator	first,
		Iterator	last
	)		-> std::unordered_map<typename std::iterator_traits<Iterator>::value_type, double>

Return relative frequency for each value.

Calculates the relative frequency by dividing each value's frequency by the total count.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator
last	Ending iterator

Returns

Map of values and their relative frequencies

Definition at line 232 of file frequency_distribution.hpp.

relative_frequency() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::relative_frequency	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)		-> std::unordered_map<std::invoke_result_t<Projection, typename std::iterator_traits<Iterator>::value_type>, double>

Relative frequency with projection.

Returns the relative frequency of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator
last	Ending iterator
proj	Projection function

Returns

Map of values and their relative frequencies

Definition at line 266 of file frequency_distribution.hpp.

relative_risk() [1/2]

relative_risk_result statcpp::relative_risk ( const std::vector< std::vector< std::size_t > > &  table )

inline

Calculate relative risk (risk ratio) from a 2x2 contingency table.

Calculates the relative risk and its confidence interval. Relative risk = (a/(a+b)) / (c/(c+d))

Standard error is calculated on the log scale (Greenland-Robins method): SE(log RR) = sqrt((1-p1)/(n1*p1) + (1-p0)/(n0*p0)) = sqrt((1-p1)/a + (1-p0)/c) where p1 = a/(a+b), p0 = c/(c+d)

Parameters

table

2x2 contingency table in the form [[a, b], [c, d]] a: Exposed and diseased b: Exposed and not diseased c: Not exposed and diseased d: Not exposed and not diseased

Returns

Relative risk calculation result

Exceptions

std::invalid_argument

If table is not 2x2, if row total is zero, or if risk is zero

Definition at line 191 of file categorical.hpp.

relative_risk() [2/2]

relative_risk_result statcpp::relative_risk ( std::size_t  a, std::size_t  b, std::size_t  c, std::size_t  d  )

inline

Calculate relative risk from a 2x2 contingency table (specifying cell values directly)

Parameters

a	Exposed and diseased
b	Exposed and not diseased
c	Not exposed and diseased
d	Not exposed and not diseased

Returns

Relative risk calculation result

Exceptions

std::invalid_argument

If row total is zero or if risk is zero

Definition at line 239 of file categorical.hpp.

ridge_regression()

regularized_regression_result statcpp::ridge_regression ( const std::vector< std::vector< double > > &  X, const std::vector< double > &  y, double  lambda, bool  standardize = true, std::size_t  max_iter = 1000, double  tol = 1e-6  )

inline

Perform Ridge regression (L2 regularization)

Solves Ridge regression using coordinate descent. L2 penalty shrinks coefficients and handles multicollinearity.

Parameters

X	Predictor matrix (each row is one sample, no intercept column)
y	Response variable vector
lambda	Regularization parameter (>= 0)
standardize	Whether to standardize data (default: true)
max_iter	Maximum number of iterations (default: 1000)
tol	Convergence tolerance (default: 1e-6)

Returns

Regularized regression result

Exceptions

std::invalid_argument

If lambda is negative, data is empty, or X and y have different sizes

Definition at line 463 of file model_selection.hpp.

risk_difference() [1/2]

risk_difference_result statcpp::risk_difference ( const std::vector< std::vector< std::size_t > > &  table )

inline

Calculate risk difference from a 2x2 contingency table.

Calculates the risk difference (attributable risk) and its confidence interval. Risk difference = (a/(a+b)) - (c/(c+d))

Parameters

table

2x2 contingency table in the form [[a, b], [c, d]]

Returns

Risk difference calculation result

Exceptions

std::invalid_argument

If table is not 2x2 or if row total is zero

Definition at line 268 of file categorical.hpp.

risk_difference() [2/2]

risk_difference_result statcpp::risk_difference ( std::size_t  a, std::size_t  b, std::size_t  c, std::size_t  d  )

inline

Calculate risk difference from a 2x2 contingency table (specifying cell values directly)

Parameters

a	Exposed and diseased
b	Exposed and not diseased
c	Not exposed and diseased
d	Not exposed and not diseased

Returns

Risk difference calculation result

Exceptions

std::invalid_argument

If row total is zero

Definition at line 312 of file categorical.hpp.

risk_ratio()

double statcpp::risk_ratio ( double  a, double  b, double  c, double  d  )

inline

Relative risk (risk ratio)

Calculates the relative risk from a 2x2 contingency table.

Parameters

a	Cell (1,1) frequency (exposed, disease present)
b	Cell (1,2) frequency (exposed, disease absent)
c	Cell (2,1) frequency (unexposed, disease present)
d	Cell (2,2) frequency (unexposed, disease absent)

Returns

Relative risk

Exceptions

std::invalid_argument

If row total is zero or risk in group 2 is zero

Definition at line 402 of file effect_size.hpp.

rmse()

template<typename Iterator1 , typename Iterator2 >

double statcpp::rmse	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2
	)

Root Mean Squared Error (RMSE)

Template Parameters

Iterator1	RandomAccessIterator type for actual values
Iterator2	RandomAccessIterator type for predicted values

Parameters

first1	Beginning iterator of actual values
last1	End iterator of actual values
first2	Beginning iterator of predicted values

Returns

RMSE

Exceptions

std::invalid_argument

If range is empty

Definition at line 266 of file time_series.hpp.

rolling_max()

std::vector< double > statcpp::rolling_max ( const std::vector< double > &  data, std::size_t  window  )

inline

Moving maximum.

Parameters

data	Data vector
window	Window size

Returns

Vector of moving maximums

Definition at line 885 of file data_wrangling.hpp.

rolling_mean()

std::vector< double > statcpp::rolling_mean ( const std::vector< double > &  data, std::size_t  window  )

inline

Moving average.

Parameters

data	Data vector
window	Window size

Returns

Vector of moving averages

Definition at line 788 of file data_wrangling.hpp.

rolling_min()

std::vector< double > statcpp::rolling_min ( const std::vector< double > &  data, std::size_t  window  )

inline

Moving minimum.

Parameters

data	Data vector
window	Window size

Returns

Vector of moving minimums

Definition at line 862 of file data_wrangling.hpp.

rolling_std()

std::vector< double > statcpp::rolling_std ( const std::vector< double > &  data, std::size_t  window  )

inline

Moving standard deviation.

Parameters

data	Data vector
window	Window size

Returns

Vector of moving standard deviations

Definition at line 833 of file data_wrangling.hpp.

rolling_sum()

std::vector< double > statcpp::rolling_sum ( const std::vector< double > &  data, std::size_t  window  )

inline

Moving sum.

Parameters

data	Data vector
window	Window size

Returns

Vector of moving sums

Definition at line 908 of file data_wrangling.hpp.

safe_divide()

double statcpp::safe_divide ( double  numerator, double  denominator, double  default_value = std::numeric_limits<double>::quiet_NaN()  )

inline

Safe division with check for division by zero.

Parameters

numerator	Numerator
denominator	Denominator
default_value	Value to return if denominator is zero (default: NaN)

Returns

numerator / denominator, or default_value if denominator is zero

Definition at line 243 of file numerical_utils.hpp.

sample_covariance() [1/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::sample_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Sample covariance (unbiased covariance)

Computes the sample covariance (unbiased estimator) of two variables. s_xy = (1/(n-1)) * sum((x_i - x_bar)(y_i - y_bar))

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Sample covariance

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 172 of file correlation_covariance.hpp.

sample_covariance() [2/3]

template<typename Iterator1 , typename Iterator2 >

double statcpp::sample_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		double	mean_x,
		double	mean_y
	)

Sample covariance with precomputed means.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
mean_x	Mean of the first data
mean_y	Mean of the second data

Returns

Sample covariance

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 216 of file correlation_covariance.hpp.

sample_covariance() [3/3]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::sample_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Sample covariance (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Sample covariance

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 260 of file correlation_covariance.hpp.

sample_kurtosis() [1/4]

template<typename Iterator >

double statcpp::sample_kurtosis	(	Iterator	first,
		Iterator	last
	)

Calculate sample kurtosis (bias-corrected version)

Calculates the bias-corrected kurtosis estimate from a sample.

Formula: G2 = ((n+1) * g2 + 6) * (n-1) / ((n-2)(n-3)) where g2 is the population kurtosis estimator (excess kurtosis)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Sample kurtosis value

Exceptions

std::invalid_argument

If number of elements is less than 4

Definition at line 535 of file shape_of_distribution.hpp.

sample_kurtosis() [2/4]

template<typename Iterator >

double statcpp::sample_kurtosis	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate sample kurtosis with precomputed mean.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Sample kurtosis value

Exceptions

std::invalid_argument

If number of elements is less than 4

Definition at line 559 of file shape_of_distribution.hpp.

sample_kurtosis() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::sample_kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate sample kurtosis with projection.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Sample kurtosis value

Exceptions

std::invalid_argument

If number of elements is less than 4

Definition at line 587 of file shape_of_distribution.hpp.

sample_kurtosis() [4/4]

template<typename Iterator , typename Projection >

double statcpp::sample_kurtosis	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate sample kurtosis with projection and precomputed mean.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample kurtosis value

Exceptions

std::invalid_argument

If number of elements is less than 4

Definition at line 613 of file shape_of_distribution.hpp.

sample_size_for_moe_mean()

std::size_t statcpp::sample_size_for_moe_mean ( double  margin_of_error, double  sigma, double  confidence_level = 0.95  )

inline

Calculate sample size for mean estimation (known population standard deviation)

Calculates the sample size required to achieve the specified margin of error. n = (z_{alpha/2} * sigma / MoE)^2

Parameters

margin_of_error	Target margin of error
sigma	Population standard deviation (known or estimated)
confidence_level	Confidence level (default: 0.95)

Returns

Required sample size

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 627 of file estimation.hpp.

sample_size_for_moe_proportion()

std::size_t statcpp::sample_size_for_moe_proportion ( double  margin_of_error, double  confidence_level = 0.95, double  p_estimate = 0.5  )

inline

Calculate sample size for proportion estimation.

Calculates the sample size required to achieve the specified margin of error. n = (z_{alpha/2} / MoE)^2 * p(1-p)

Parameters

margin_of_error	Target margin of error
confidence_level	Confidence level (default: 0.95)
p_estimate	Prior estimate of proportion (default: 0.5 for most conservative estimate)

Returns

Required sample size

Exceptions

std::invalid_argument

If parameters are outside valid range

Definition at line 591 of file estimation.hpp.

sample_size_prop_test() [1/2]

std::size_t statcpp::sample_size_prop_test ( double  p1, double  p2, double  power, double  alpha, alternative_hypothesis  alt  )

inline

Calculate required sample size for two-sample proportion test (enum overload)

Parameters

p1	Proportion of group 1
p2	Proportion of group 2
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Required sample size per group

Definition at line 599 of file power_analysis.hpp.

sample_size_prop_test() [2/2]

std::size_t statcpp::sample_size_prop_test ( double  p1, double  p2, double  power = 0.80, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Calculate required sample size for two-sample proportion test.

Parameters

p1	Proportion of group 1
p2	Proportion of group 2
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Required sample size per group

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 409 of file power_analysis.hpp.

sample_size_t_test_one_sample() [1/2]

std::size_t statcpp::sample_size_t_test_one_sample ( double  effect_size, double  power, double  alpha, alternative_hypothesis  alt  )

inline

Calculate required sample size for one-sample t-test (enum overload)

Parameters

effect_size	Effect size (Cohen's d)
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Required sample size

Definition at line 531 of file power_analysis.hpp.

sample_size_t_test_one_sample() [2/2]

std::size_t statcpp::sample_size_t_test_one_sample ( double  effect_size, double  power = 0.80, double  alpha = 0.05, const std::string &  alternative = "two.sided"  )

inline

Calculate required sample size for one-sample t-test.

Parameters

effect_size	Effect size (Cohen's d)
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Required sample size

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 195 of file power_analysis.hpp.

sample_size_t_test_two_sample() [1/2]

std::size_t statcpp::sample_size_t_test_two_sample ( double  effect_size, double  power, double  alpha, double  ratio, alternative_hypothesis  alt  )

inline

Calculate required sample size for two-sample t-test (enum overload)

Parameters

effect_size	Effect size (Cohen's d)
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
ratio	Ratio n2/n1 (default: 1.0)
alt	Type of alternative hypothesis (default: two_sided)

Returns

Required sample size for group 1

Definition at line 565 of file power_analysis.hpp.

sample_size_t_test_two_sample() [2/2]

std::size_t statcpp::sample_size_t_test_two_sample ( double  effect_size, double  power = 0.80, double  alpha = 0.05, double  ratio = 1.0, const std::string &  alternative = "two.sided"  )

inline

Calculate required sample size for two-sample t-test (per group)

Parameters

effect_size	Effect size (Cohen's d)
power	Target power (default: 0.80)
alpha	Significance level (default: 0.05)
ratio	Ratio n2/n1 (default: 1.0 = equal sizes)
alternative	Type of alternative hypothesis (default: "two.sided")

Returns

Required sample size for group 1 (group 2 size is n1 * ratio)

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 295 of file power_analysis.hpp.

sample_skewness() [1/4]

template<typename Iterator >

double statcpp::sample_skewness	(	Iterator	first,
		Iterator	last
	)

Calculate sample skewness (bias-corrected version)

Calculates the bias-corrected skewness estimate from a sample.

Formula: G1 = sqrt(n(n-1)) / (n-2) * g1 where g1 is the population skewness estimator

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Sample skewness value

Exceptions

std::invalid_argument

If number of elements is less than 3

Definition at line 202 of file shape_of_distribution.hpp.

sample_skewness() [2/4]

template<typename Iterator >

double statcpp::sample_skewness	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate sample skewness with precomputed mean.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Sample skewness value

Exceptions

std::invalid_argument

If number of elements is less than 3

Definition at line 225 of file shape_of_distribution.hpp.

sample_skewness() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::sample_skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate sample skewness with projection.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Sample skewness value

Exceptions

std::invalid_argument

If number of elements is less than 3

Definition at line 252 of file shape_of_distribution.hpp.

sample_skewness() [4/4]

template<typename Iterator , typename Projection >

double statcpp::sample_skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate sample skewness with projection and precomputed mean.

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample skewness value

Exceptions

std::invalid_argument

If number of elements is less than 3

Definition at line 277 of file shape_of_distribution.hpp.

sample_stddev() [1/4]

template<typename Iterator >

double statcpp::sample_stddev	(	Iterator	first,
		Iterator	last
	)

Sample standard deviation.

Computes the sample standard deviation (square root of variance divided by N-1).

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Sample standard deviation

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 669 of file dispersion_spread.hpp.

sample_stddev() [2/4]

template<typename Iterator >

double statcpp::sample_stddev	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Sample standard deviation using precomputed mean.

Computes sample standard deviation when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Sample standard deviation

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 687 of file dispersion_spread.hpp.

sample_stddev() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::sample_stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Sample standard deviation of projected values using a lambda expression.

Computes the sample standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Sample standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 709 of file dispersion_spread.hpp.

sample_stddev() [4/4]

template<typename Iterator , typename Projection >

double statcpp::sample_stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Sample standard deviation of projected values using precomputed mean.

Computes sample standard deviation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 729 of file dispersion_spread.hpp.

sample_variance() [1/4]

template<typename Iterator >

double statcpp::sample_variance	(	Iterator	first,
		Iterator	last
	)

Sample variance (unbiased variance)

Computes the unbiased sample variance (divide by N-1).

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Sample variance

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 339 of file dispersion_spread.hpp.

sample_variance() [2/4]

template<typename Iterator >

double statcpp::sample_variance	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Sample variance using precomputed mean.

Computes sample variance when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Sample variance

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 357 of file dispersion_spread.hpp.

sample_variance() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::sample_variance	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Sample variance of projected values using a lambda expression.

Computes the sample variance of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Sample variance of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 379 of file dispersion_spread.hpp.

sample_variance() [4/4]

template<typename Iterator , typename Projection >

double statcpp::sample_variance	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Sample variance of projected values using precomputed mean.

Computes sample variance using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample variance of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 399 of file dispersion_spread.hpp.

sample_with_replacement()

template<typename T >

std::vector< T > statcpp::sample_with_replacement	(	const std::vector< T > &	data,
		std::size_t	n
	)

Random sampling (with replacement)

Template Parameters

T

Data type

Parameters

data	Data vector
n	Sample size

Returns

Sampled data

Definition at line 625 of file data_wrangling.hpp.

sample_without_replacement()

template<typename T >

std::vector< T > statcpp::sample_without_replacement	(	const std::vector< T > &	data,
		std::size_t	n
	)

Random sampling (without replacement)

Template Parameters

T

Data type

Parameters

data	Data vector
n	Sample size

Returns

Sampled data

Definition at line 651 of file data_wrangling.hpp.

scheffe_posthoc()

posthoc_result statcpp::scheffe_posthoc ( const one_way_anova_result &  anova_result, double  alpha = 0.05  )

inline

Perform Scheffe's method for multiple comparisons.

Performs multiple comparisons among all pairs of groups using Scheffe's method as a post-hoc test following one-way ANOVA. This is the most conservative method.

Scheffe's method is valid for any linear contrast, applicable not only to pairwise comparisons but also to complex contrasts. The F statistic is calculated as t^2 / (k-1) and compared to F(k-1, df_error) distribution. The p-value is computed as 1 - F_cdf(F_s, k-1, df_error).

Parameters

anova_result	Result from one-way ANOVA
alpha	Significance level (default: 0.05)

Returns

posthoc_result Post-hoc comparison results

Exceptions

std::invalid_argument

If alpha is outside the range (0, 1)

Definition at line 591 of file anova.hpp.

seasonal_diff()

template<typename Iterator >

std::vector< double > statcpp::seasonal_diff	(	Iterator	first,
		Iterator	last,
		std::size_t	period
	)

Seasonal differencing.

Calculates the seasonal difference for time series data with seasonality.

Template Parameters

Iterator

RandomAccessIterator type

Parameters

first	Beginning iterator
last	End iterator
period	Seasonal period

Returns

Vector of seasonal differenced series

Exceptions

std::invalid_argument

If data is insufficient for the period

Definition at line 455 of file time_series.hpp.

sensitivity_analysis_pattern_mixture()

sensitivity_analysis_result statcpp::sensitivity_analysis_pattern_mixture ( const std::vector< double > &  data, const std::vector< double > &  delta_values  )

inline

Sensitivity analysis using pattern mixture model.

Evaluates robustness of estimates by varying the difference (delta) between missing and observed values under MNAR (Missing Not At Random) assumption.

Basic formula of pattern mixture model:

• E[Y] = E[Y|R=1] * P(R=1) + E[Y|R=0] * P(R=0)
• where R=1 indicates observed, R=0 indicates missing
• Sensitivity parameter delta: E[Y|R=0] = E[Y|R=1] + delta

Interpretation of delta:

• delta = 0: MAR (missing follows same distribution as observed)
• delta > 0: Missing values tend to be higher than observed
• delta < 0: Missing values tend to be lower than observed

Note

This implementation uses a simplified assumption for variance (equal to observed variance). More rigorous analysis requires pattern-specific variance estimation.

Parameters

data	1D data for analysis
delta_values	Vector of sensitivity parameter delta values

Returns

sensitivity_analysis_result Sensitivity analysis result

Exceptions

std::invalid_argument

If data is empty or all values are missing

Definition at line 810 of file missing_data.hpp.

sensitivity_analysis_selection_model()

sensitivity_analysis_result statcpp::sensitivity_analysis_selection_model ( const std::vector< double > &  data, const std::vector< double > &  phi_values  )

inline

Sensitivity analysis using selection model.

Evaluates robustness of estimates by varying the degree (phi) to which missingness depends on the response value. phi = 0 corresponds to MAR assumption, and phi > 0 indicates that missing values tend to be lower than observed values.

Parameters

data	1D data for analysis
phi_values	Vector of sensitivity parameter phi values

Returns

sensitivity_analysis_result Sensitivity analysis result

Exceptions

std::invalid_argument

If data is empty or all values are missing

Definition at line 888 of file missing_data.hpp.

set_seed()

void statcpp::set_seed ( std::uint64_t  seed )

inline

Set the seed of the random engine.

Sets the seed of the global random engine to the specified value. Use this when reproducible random sequences are needed.

Parameters

seed	Seed value to set

Definition at line 45 of file random_engine.hpp.

shapiro_wilk_test()

template<typename Iterator >

test_result statcpp::shapiro_wilk_test	(	Iterator	first,
		Iterator	last
	)

Perform Shapiro-Wilk test.

Tests whether data follows a normal distribution. Uses Royston's algorithm for approximation. Optimized for sample sizes n <= 50, but supports up to n <= 5000.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of range
last	Ending iterator of range

Returns

test_result Test result containing W statistic, p-value, and sample size

Exceptions

std::invalid_argument	If there are fewer than 3 elements
std::invalid_argument	If there are more than 5000 elements
std::invalid_argument	If variance is zero

Note

Null hypothesis: Data follows a normal distribution

W statistic closer to 1 indicates higher normality

Definition at line 144 of file nonparametric_tests.hpp.

silhouette_score()

double statcpp::silhouette_score ( const std::vector< std::vector< double > > &  data, const std::vector< std::size_t > &  labels  )

inline

Calculate silhouette score.

Calculates the silhouette score to evaluate clustering quality.

Parameters

data	Vector of data points
labels	Cluster labels

Returns

Silhouette score (-1 to 1, closer to 1 is better)

Exceptions

std::invalid_argument

If data is empty or sizes don't match

Note

Score interpretation: 0.7-1.0: strong structure, 0.5-0.7: reasonable structure, 0.25-0.5: weak structure, < 0.25: no substantial structure

Definition at line 498 of file clustering.hpp.

simple_linear_regression()

template<typename IteratorX , typename IteratorY >

simple_regression_result statcpp::simple_linear_regression	(	IteratorX	x_first,
		IteratorX	x_last,
		IteratorY	y_first,
		IteratorY	y_last
	)

Perform simple linear regression.

Estimates simple regression model y = b0 + b1*x using least squares method. Calculates regression coefficients, standard errors, t-tests, F-test, and coefficient of determination.

Template Parameters

IteratorX	Iterator type for predictor variable
IteratorY	Iterator type for response variable

Parameters

x_first	Beginning iterator for predictor variable
x_last	Ending iterator for predictor variable
y_first	Beginning iterator for response variable
y_last	Ending iterator for response variable

Returns

simple_regression_result Regression analysis results

Exceptions

std::invalid_argument	If x and y have different lengths
std::invalid_argument	If there are fewer than 3 observations
std::invalid_argument	If x has zero variance

Definition at line 128 of file linear_regression.hpp.

skewness() [1/4]

template<typename Iterator >

double statcpp::skewness	(	Iterator	first,
		Iterator	last
	)

Calculate skewness (alias for sample_skewness)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range

Returns

Sample skewness value

Definition at line 298 of file shape_of_distribution.hpp.

skewness() [2/4]

template<typename Iterator >

double statcpp::skewness	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Calculate skewness (precomputed mean version)

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
precomputed_mean	Precomputed mean value

Returns

Sample skewness value

Definition at line 313 of file shape_of_distribution.hpp.

skewness() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate skewness (projection version)

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function

Returns

Sample skewness value

Definition at line 332 of file shape_of_distribution.hpp.

skewness() [4/4]

template<typename Iterator , typename Projection >

double statcpp::skewness	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Calculate skewness (projection version, precomputed mean)

Template Parameters

Iterator	Input iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	End iterator of data range
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Sample skewness value

Definition at line 349 of file shape_of_distribution.hpp.

sort_values()

template<typename T >

std::vector< T > statcpp::sort_values	(	const std::vector< T > &	data,
		bool	ascending = true
	)

Return a sorted vector (ascending)

Template Parameters

T

Data type

Parameters

data	Data vector
ascending	true for ascending, false for descending

Returns

Sorted vector

Definition at line 579 of file data_wrangling.hpp.

spearman_correlation() [1/2]

template<typename Iterator1 , typename Iterator2 >

double statcpp::spearman_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2
	)

Spearman's rank correlation coefficient.

Computes Spearman's rank correlation coefficient of two variables. rho = Pearson(rank(X), rank(Y)) Applies Pearson correlation coefficient to ranked data. Can detect monotonic relationships and is robust to outliers.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data

Returns

Spearman's rank correlation coefficient (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 650 of file correlation_covariance.hpp.

spearman_correlation() [2/2]

template<typename Iterator1 , typename Iterator2 , typename Projection1 , typename Projection2 >

double statcpp::spearman_correlation	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		Projection1	proj1,
		Projection2	proj2
	)

Spearman's rank correlation coefficient (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Spearman's rank correlation coefficient (-1 to 1)

Exceptions

std::invalid_argument

If range is empty, lengths differ, or number of elements is less than 2

Definition at line 690 of file correlation_covariance.hpp.

sqrt_transform()

std::vector< double > statcpp::sqrt_transform ( const std::vector< double > &  data )

inline

Square root transformation.

Parameters

data	Data vector

Returns

Square root-transformed data (negative values become NA)

Definition at line 366 of file data_wrangling.hpp.

standard_error() [1/3]

template<typename Iterator >

double statcpp::standard_error	(	Iterator	first,
		Iterator	last
	)

Calculate standard error of the mean.

Standard error: SE = s / sqrt(n)

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range

Returns

Standard error

Exceptions

std::invalid_argument

If there are fewer than 2 elements

Definition at line 38 of file estimation.hpp.

standard_error() [2/3]

template<typename Iterator >

double statcpp::standard_error	(	Iterator	first,
		Iterator	last,
		double	precomputed_stddev
	)

Calculate standard error of the mean (using precomputed standard deviation)

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
precomputed_stddev	Precomputed standard deviation

Returns

Standard error

Exceptions

std::invalid_argument

If the range is empty

Definition at line 81 of file estimation.hpp.

standard_error() [3/3]

template<typename Iterator , typename Projection >

double statcpp::standard_error	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Calculate standard error of the mean (projection version)

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Beginning iterator of data range
last	Ending iterator of data range
proj	Projection function

Returns

Standard error

Exceptions

std::invalid_argument

If there are fewer than 2 elements

Definition at line 60 of file estimation.hpp.

standardize()

std::vector< std::vector< double > > statcpp::standardize ( const std::vector< std::vector< double > > &  data )

inline

Z-score standardization.

Standardizes each variable to mean 0 and standard deviation 1. Data is passed with rows=observations and columns=variables.

Parameters

data	Matrix data (rows=observations, columns=variables)

Returns

Standardized data

Exceptions

std::invalid_argument

If data is empty, rows have different column counts, there are fewer than 2 observations, or any variable has zero variance

Definition at line 139 of file multivariate.hpp.

stddev() [1/4]

template<typename Iterator >

double statcpp::stddev	(	Iterator	first,
		Iterator	last
	)

Standard deviation (alias for sample_stddev)

Computes sample standard deviation. Equivalent to sample_stddev.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Standard deviation

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 750 of file dispersion_spread.hpp.

stddev() [2/4]

template<typename Iterator >

double statcpp::stddev	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Standard deviation using precomputed mean.

Computes sample standard deviation when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Standard deviation

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 768 of file dispersion_spread.hpp.

stddev() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Standard deviation of projected values using a lambda expression.

Computes the sample standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 790 of file dispersion_spread.hpp.

stddev() [4/4]

template<typename Iterator , typename Projection >

double statcpp::stddev	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Standard deviation of projected values using precomputed mean.

Computes sample standard deviation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Standard deviation of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 810 of file dispersion_spread.hpp.

stdev() [1/4]

template<typename Iterator >

double statcpp::stdev	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean,
		std::size_t	ddof
	)

Standard deviation using precomputed mean (with ddof)

Use when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value
ddof	Degrees of freedom correction (0 or 1)

Returns

Standard deviation

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 523 of file dispersion_spread.hpp.

stdev() [2/4]

template<typename Iterator , typename Projection >

double statcpp::stdev	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean,
		std::size_t	ddof
	)

Standard deviation of projected values using precomputed mean (with ddof)

Computes standard deviation using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value
ddof	Degrees of freedom correction (0 or 1)

Returns

Standard deviation of projected values

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 567 of file dispersion_spread.hpp.

stdev() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::stdev	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		std::size_t	ddof = 0
	)

Standard deviation of projected values using a lambda expression (with ddof)

Computes the standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
ddof	Degrees of freedom correction (0 or 1)

Returns

Standard deviation of projected values

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 546 of file dispersion_spread.hpp.

stdev() [4/4]

template<typename Iterator >

double statcpp::stdev	(	Iterator	first,
		Iterator	last,
		std::size_t	ddof = 0
	)

Standard deviation (ddof = Delta Degrees of Freedom)

ddof = 0: Population standard deviation (square root of variance divided by N) ddof = 1: Sample standard deviation (square root of variance divided by N-1) Behaves like NumPy's np.std(a, ddof=...).

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
ddof	Degrees of freedom correction (0 or 1)

Returns

Standard deviation

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 504 of file dispersion_spread.hpp.

stratified_sample()

template<typename K , typename V >

std::vector< V > statcpp::stratified_sample	(	const std::vector< K > &	strata,
		const std::vector< V > &	data,
		double	sample_ratio
	)

Stratified sampling.

Template Parameters

K	Stratum type
V	Data type

Parameters

strata	Vector of strata
data	Data vector
sample_ratio	Sampling ratio

Returns

Stratified sampled data

Definition at line 682 of file data_wrangling.hpp.

studentized_range_cdf()

double statcpp::studentized_range_cdf ( double  q, double  k, double  df  )

inline

CDF of the studentized range distribution.

Computes P(Q <= q) where Q follows the studentized range distribution with k groups and df degrees of freedom.

Uses the Copenhaver & Holland (1988) algorithm with nested Gauss-Legendre quadrature, equivalent to R's ptukey().

Parameters

q	Quantile value
k	Number of groups (must be >= 2)
df	Degrees of freedom (must be > 0)

Returns

Probability P(Q <= q)

Exceptions

std::invalid_argument

If k < 2 or df <= 0

Definition at line 1235 of file continuous_distributions.hpp.

studentized_range_quantile()

double statcpp::studentized_range_quantile ( double  p, double  k, double  df  )

inline

Quantile function of the studentized range distribution.

Computes q such that P(Q <= q) = p where Q follows the studentized range distribution with k groups and df degrees of freedom.

Uses Newton-Raphson iteration with numerical differentiation (central difference).

Parameters

p	Probability (must be in [0, 1])
k	Number of groups (must be >= 2)
df	Degrees of freedom (must be > 0)

Returns

Quantile value

Exceptions

std::invalid_argument

If k < 2, df <= 0, or p is outside [0, 1]

Note

Uses Newton-Raphson iteration with tolerance eps = 1e-10 and maximum 50 iterations. If the iteration does not converge within the maximum number of iterations, the best approximation so far is returned (no exception is thrown). For interior points (0 < p < 1), the result is a finite value. Boundary values p = 0 or p = 1 may return +/-infinity as per the distribution definition. In practice, convergence is achieved for all typical input ranges.

Definition at line 1460 of file continuous_distributions.hpp.

sum() [1/2]

template<typename Iterator >

auto statcpp::sum	(	Iterator	first,
		Iterator	last
	)

Sum.

Computes the sum of all elements in the range.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Sum value

Definition at line 46 of file basic_statistics.hpp.

sum() [2/2]

template<typename Iterator , typename Projection >

auto statcpp::sum	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Sum of projected values using a lambda expression.

Computes the sum of the results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Sum of projected values

Definition at line 65 of file basic_statistics.hpp.

t_cdf()

double statcpp::t_cdf ( double  x, double  df  )

inline

t-distribution cumulative distribution function (CDF)

Computed using the regularized incomplete beta function. The CDF of t-distribution is expressed as:

F(x; nu) = 1 - 0.5 * I_{nu/(nu+x^2)}(nu/2, 1/2) (for x >= 0) F(x; nu) = 0.5 * I_{nu/(nu+x^2)}(nu/2, 1/2) (for x < 0)

where I_z(a,b) is the regularized incomplete beta function and nu is degrees of freedom. This transformation enables efficient computation of t-distribution CDF via beta distribution CDF.

Parameters

x	Random variable value
df	Degrees of freedom nu

Returns

Cumulative probability

Exceptions

std::invalid_argument

If df <= 0

Definition at line 707 of file continuous_distributions.hpp.

t_pdf()

double statcpp::t_pdf ( double  x, double  df  )

inline

t-distribution probability density function (PDF)

f(x) = Gamma((nu+1)/2) / (sqrt(nu*pi) * Gamma(nu/2)) * (1 + x^2/nu)^(-(nu+1)/2)

Parameters

x	Random variable value
df	Degrees of freedom

Returns

Probability density

Exceptions

std::invalid_argument

If df <= 0

Definition at line 680 of file continuous_distributions.hpp.

t_quantile()

double statcpp::t_quantile ( double  p, double  df  )

inline

t-distribution quantile function (Newton-Raphson method)

Parameters

p	Probability (0 < p < 1)
df	Degrees of freedom

Returns

Quantile

Exceptions

std::invalid_argument

If df <= 0 or p is outside (0, 1)

Note

Uses Newton-Raphson iteration with tolerance eps = 1e-10 and maximum 50 iterations. If the iteration does not converge within the maximum number of iterations, the best approximation so far is returned (no exception is thrown). For interior points (0 < p < 1), the result is a finite value. Boundary values p = 0 or p = 1 may return +/-infinity as per the distribution definition. In practice, convergence is achieved for all typical input ranges.

Definition at line 739 of file continuous_distributions.hpp.

t_rand() [1/2]

double statcpp::t_rand ( double  df )

inline

t-distribution random number generation (using default engine)

Parameters

df	Degrees of freedom

Returns

Random number following t-distribution

Definition at line 812 of file continuous_distributions.hpp.

t_rand() [2/2]

template<typename Engine = default_random_engine>

double statcpp::t_rand	(	double	df,
		Engine &	engine
	)

t-distribution random number generation

Template Parameters

Engine

Random engine type

Parameters

df	Degrees of freedom
engine	Random engine

Returns

Random number following t-distribution

Exceptions

std::invalid_argument

If df <= 0

Definition at line 797 of file continuous_distributions.hpp.

t_test()

template<typename Iterator >

test_result statcpp::t_test	(	Iterator	first,
		Iterator	last,
		double	mu0,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

One-sample t-test.

Tests whether the sample mean equals a specific value (unknown population variance).

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of sample data
last	End iterator of sample data
mu0	Population mean under null hypothesis
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (t-statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If number of elements is less than 2 or variance is zero

Definition at line 231 of file parametric_tests.hpp.

t_test_paired()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::t_test_paired	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

Paired t-test.

Tests whether the mean of differences between two paired samples equals zero.

Template Parameters

Iterator1	Input iterator type for first sample
Iterator2	Input iterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (t-statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If sample lengths differ or are less than 2

Definition at line 415 of file parametric_tests.hpp.

t_test_two_sample()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::t_test_two_sample	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

Two-sample t-test (independent samples, pooled variance)

Tests whether the means of two independent samples are equal. Assumes equal variance and uses pooled variance.

Template Parameters

Iterator1	Input iterator type for first sample
Iterator2	Input iterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (t-statistic, p-value, degrees of freedom)

Exceptions

std::invalid_argument

If either sample has less than 2 elements or variance is zero

Definition at line 284 of file parametric_tests.hpp.

t_test_welch()

template<typename Iterator1 , typename Iterator2 >

test_result statcpp::t_test_welch	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

Two-sample t-test (Welch's method)

Tests whether the means of two independent samples are equal. Does not assume equal variance; uses Welch-Satterthwaite approximation for degrees of freedom.

Template Parameters

Iterator1	Input iterator type for first sample
Iterator2	Input iterator type for second sample

Parameters

first1	Beginning iterator of first sample
last1	End iterator of first sample
first2	Beginning iterator of second sample
last2	End iterator of second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (t-statistic, p-value, Welch approximation degrees of freedom)

Exceptions

std::invalid_argument

If either sample has less than 2 elements or variance is zero

Definition at line 345 of file parametric_tests.hpp.

t_to_r()

double statcpp::t_to_r ( double  t, double  df  )

inline

Convert t-value to correlation coefficient.

Parameters

t	t-statistic
df	Degrees of freedom

Returns

Correlation coefficient

Definition at line 249 of file effect_size.hpp.

test_mcar_simple()

mcar_test_result statcpp::test_mcar_simple ( const std::vector< std::vector< double > > &  data )

inline

Little's MCAR test (simplified version)

Tests whether the mean difference between complete and incomplete data is significant, determining if data is MCAR (Missing Completely At Random).

Note

This is a simplified version; the complete Little's test requires covariance estimation via EM algorithm.

Parameters

data	2D data for testing (rows: observations, columns: variables)

Returns

mcar_test_result Test result (chi-square statistic, p-value, degrees of freedom, conclusion)

Exceptions

std::invalid_argument

If data is empty

Definition at line 209 of file missing_data.hpp.

tgamma()

double statcpp::tgamma ( double  x )

inline

Gamma function.

Computes the gamma function Gamma(x).

Parameters

x

Argument

Returns

Gamma(x)

Exceptions

std::domain_error

If x is a non-positive integer

Note

For small positive integers, computes factorial directly.

Definition at line 116 of file special_functions.hpp.

trimmed_mean() [1/2]

template<typename Iterator >

double statcpp::trimmed_mean	(	Iterator	first,
		Iterator	last,
		double	proportion
	)

Trimmed mean (accepts a sorted range. proportion: exclusion ratio per side, 0.0 to less than 0.5)

Computes the mean after excluding a certain proportion of data from both ends. Useful for reducing the influence of outliers.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
proportion	Exclusion ratio per side (0.0 to less than 0.5)

Returns

Trimmed mean

Exceptions

std::invalid_argument

If range is empty, proportion is out of range, or all elements are excluded

Definition at line 590 of file basic_statistics.hpp.

trimmed_mean() [2/2]

template<typename Iterator , typename Projection >

double statcpp::trimmed_mean	(	Iterator	first,
		Iterator	last,
		double	proportion,
		Projection	proj
	)

Trimmed mean of projected values using a lambda expression (projection results must be in sorted order)

Computes the trimmed mean of the results after applying a projection function to each element. Assumes that projection results are sorted.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proportion	Exclusion ratio per side (0.0 to less than 0.5)
proj	Projection function

Returns

Trimmed mean of projected values

Exceptions

std::invalid_argument

If range is empty, proportion is out of range, or all elements are excluded

Definition at line 634 of file basic_statistics.hpp.

tukey_hsd()

posthoc_result statcpp::tukey_hsd ( const one_way_anova_result &  anova_result, const std::vector< std::vector< double > > &  groups, double  alpha = 0.05  )

inline

Perform Tukey's Honestly Significant Difference (HSD) test.

Performs all pairwise comparisons among groups using the studentized range distribution (Tukey-Kramer method for unequal sample sizes).

The q statistic is computed as |mean_i - mean_j| / SE where SE = sqrt(MSE/2 * (1/n_i + 1/n_j)), and p-values are obtained from the studentized range distribution with k groups and df_error degrees of freedom.

Parameters

anova_result	Result from one-way ANOVA
groups	Data for each group (currently unused; retained for API compatibility and potential future use such as input validation)
alpha	Significance level (default: 0.05)

Returns

posthoc_result Post-hoc comparison results (statistic field contains q statistic)

Exceptions

std::invalid_argument

If alpha is outside the range (0, 1)

Definition at line 370 of file anova.hpp.

two_way_anova()

two_way_anova_result statcpp::two_way_anova ( const std::vector< std::vector< std::vector< double > > > &  data )

inline

Perform two-way analysis of variance (with replication)

Tests the effects of two factors (A, B) and their interaction on the dependent variable. Assumes equal cell sizes.

Parameters

data	3-dimensional data array. data[i][j] is the vector of observations for factor A=i, factor B=j

Returns

two_way_anova_result Results of the analysis of variance

Exceptions

std::invalid_argument	If number of levels for factor A is less than 2
std::invalid_argument	If number of levels for factor B is less than 2
std::invalid_argument	If number of levels for factor B is inconsistent
std::invalid_argument	If cell sizes are unequal
std::invalid_argument	If an empty cell exists

Definition at line 215 of file anova.hpp.

uniform_cdf()

double statcpp::uniform_cdf ( double  x, double  a = 0.0, double  b = 1.0  )

inline

Uniform distribution cumulative distribution function (CDF)

F(x) = (x - a) / (b - a)

Parameters

x	Random variable value
a	Lower bound (default: 0.0)
b	Upper bound (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If a >= b

Definition at line 60 of file continuous_distributions.hpp.

uniform_pdf()

double statcpp::uniform_pdf ( double  x, double  a = 0.0, double  b = 1.0  )

inline

Uniform distribution probability density function (PDF)

f(x) = 1 / (b - a) for a <= x <= b

Parameters

x	Random variable value
a	Lower bound (default: 0.0)
b	Upper bound (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If a >= b

Definition at line 38 of file continuous_distributions.hpp.

uniform_quantile()

double statcpp::uniform_quantile ( double  p, double  a = 0.0, double  b = 1.0  )

inline

Uniform distribution quantile function (inverse CDF)

Q(p) = a + p * (b - a)

Parameters

p	Probability (0 <= p <= 1)
a	Lower bound (default: 0.0)
b	Upper bound (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If a >= b or p is outside [0, 1]

Definition at line 81 of file continuous_distributions.hpp.

uniform_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::uniform_rand	(	double	a,
		double	b,
		Engine &	engine
	)

Uniform distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

a	Lower bound
b	Upper bound
engine	Random engine

Returns

Random number following uniform distribution

Exceptions

std::invalid_argument

If a >= b

Definition at line 103 of file continuous_distributions.hpp.

uniform_rand() [2/2]

double statcpp::uniform_rand ( double  a = 0.0, double  b = 1.0  )

inline

Uniform distribution random number generation (using default engine)

Parameters

a	Lower bound (default: 0.0)
b	Upper bound (default: 1.0)

Returns

Random number following uniform distribution

Definition at line 119 of file continuous_distributions.hpp.

validate_data()

validation_result statcpp::validate_data ( const std::vector< double > &  data, bool  allow_missing = false, bool  allow_infinite = false, bool  allow_negative = true  )

inline

Data validation.

Parameters

data	Data vector
allow_missing	Allow missing values
allow_infinite	Allow infinite values
allow_negative	Allow negative values

Returns

Validation result

Definition at line 1109 of file data_wrangling.hpp.

validate_range()

bool statcpp::validate_range ( const std::vector< double > &  data, double  min_val = -std::numeric_limits<double>::infinity(), double  max_val = std::numeric_limits<double>::infinity()  )

inline

Range validation.

Parameters

data	Data vector
min_val	Minimum value
max_val	Maximum value

Returns

true if all values are within range

Definition at line 1149 of file data_wrangling.hpp.

value_counts()

template<typename T >

std::map< T, std::size_t > statcpp::value_counts

(

const std::vector< T > &

data

)

Count duplicates.

Template Parameters

T

Data type

Parameters

data	Data vector

Returns

Map of values and their occurrence counts

Definition at line 744 of file data_wrangling.hpp.

var() [1/4]

template<typename Iterator >

double statcpp::var	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean,
		std::size_t	ddof
	)

Variance using precomputed mean (with ddof)

Use when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value
ddof	Degrees of freedom correction (0 or 1)

Returns

Variance

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 147 of file dispersion_spread.hpp.

var() [2/4]

template<typename Iterator , typename Projection >

double statcpp::var	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean,
		std::size_t	ddof
	)

Variance of projected values using precomputed mean (with ddof)

Computes variance using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value
ddof	Degrees of freedom correction (0 or 1)

Returns

Variance of projected values

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 222 of file dispersion_spread.hpp.

var() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::var	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		std::size_t	ddof = 0
	)

Variance of projected values using a lambda expression (with ddof)

Computes the variance of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
ddof	Degrees of freedom correction (0 or 1)

Returns

Variance of projected values

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 185 of file dispersion_spread.hpp.

var() [4/4]

template<typename Iterator >

double statcpp::var	(	Iterator	first,
		Iterator	last,
		std::size_t	ddof = 0
	)

Variance (ddof = Delta Degrees of Freedom)

ddof = 0: Population variance (divide by N) ddof = 1: Sample variance / unbiased variance (divide by N-1)

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
ddof	Degrees of freedom correction (0 or 1)

Returns

Variance

Exceptions

std::invalid_argument

If range is empty, ddof is not 0 or 1, or ddof=1 with fewer than 2 elements

Definition at line 112 of file dispersion_spread.hpp.

variance() [1/4]

template<typename Iterator >

double statcpp::variance	(	Iterator	first,
		Iterator	last
	)

Variance (alias for sample_variance)

Computes sample variance. Equivalent to sample_variance.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator

Returns

Variance

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 420 of file dispersion_spread.hpp.

variance() [2/4]

template<typename Iterator >

double statcpp::variance	(	Iterator	first,
		Iterator	last,
		double	precomputed_mean
	)

Variance using precomputed mean.

Computes sample variance when the mean has been precomputed.

Template Parameters

Iterator

Iterator type

Parameters

first	Begin iterator
last	End iterator
precomputed_mean	Precomputed mean value

Returns

Variance

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 438 of file dispersion_spread.hpp.

variance() [3/4]

template<typename Iterator , typename Projection , typename = std::enable_if_t< std::is_invocable_v<Projection, typename std::iterator_traits<Iterator>::value_type>>>

double statcpp::variance	(	Iterator	first,
		Iterator	last,
		Projection	proj
	)

Variance of projected values using a lambda expression.

Computes the sample variance of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function

Returns

Variance of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 460 of file dispersion_spread.hpp.

variance() [4/4]

template<typename Iterator , typename Projection >

double statcpp::variance	(	Iterator	first,
		Iterator	last,
		Projection	proj,
		double	precomputed_mean
	)

Variance of projected values using precomputed mean.

Computes sample variance using a projection function and precomputed mean.

Template Parameters

Iterator	Iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
proj	Projection function
precomputed_mean	Precomputed mean value

Returns

Variance of projected values

Exceptions

std::invalid_argument

If the range is empty or has fewer than 2 elements

Definition at line 480 of file dispersion_spread.hpp.

weibull_cdf()

double statcpp::weibull_cdf ( double  x, double  shape, double  scale = 1.0  )

inline

Weibull distribution cumulative distribution function (CDF)

F(x) = 1 - exp(-(x/lambda)^k)

Parameters

x	Random variable value
shape	Shape parameter k
scale	Scale parameter lambda (default: 1.0)

Returns

Cumulative probability

Exceptions

std::invalid_argument

If shape <= 0 or scale <= 0

Definition at line 1138 of file continuous_distributions.hpp.

weibull_pdf()

double statcpp::weibull_pdf ( double  x, double  shape, double  scale = 1.0  )

inline

Weibull distribution probability density function (PDF)

f(x) = (k/lambda) * (x/lambda)^(k-1) * exp(-(x/lambda)^k)

Parameters

x	Random variable value
shape	Shape parameter k
scale	Scale parameter lambda (default: 1.0)

Returns

Probability density

Exceptions

std::invalid_argument

If shape <= 0 or scale <= 0

Definition at line 1103 of file continuous_distributions.hpp.

weibull_quantile()

double statcpp::weibull_quantile ( double  p, double  shape, double  scale = 1.0  )

inline

Weibull distribution quantile function.

Q(p) = lambda * (-ln(1 - p))^(1/k)

Parameters

p	Probability (0 <= p <= 1)
shape	Shape parameter k
scale	Scale parameter lambda (default: 1.0)

Returns

Quantile

Exceptions

std::invalid_argument

If shape <= 0, scale <= 0, or p is outside [0, 1]

Definition at line 1164 of file continuous_distributions.hpp.

weibull_rand() [1/2]

template<typename Engine = default_random_engine>

double statcpp::weibull_rand	(	double	shape,
		double	scale,
		Engine &	engine
	)

Weibull distribution random number generation.

Template Parameters

Engine

Random engine type

Parameters

shape	Shape parameter k
scale	Scale parameter lambda
engine	Random engine

Returns

Random number following Weibull distribution

Exceptions

std::invalid_argument

If shape <= 0 or scale <= 0

Definition at line 1191 of file continuous_distributions.hpp.

weibull_rand() [2/2]

double statcpp::weibull_rand ( double  shape, double  scale = 1.0  )

inline

Weibull distribution random number generation (using default engine)

Parameters

shape	Shape parameter k
scale	Scale parameter lambda (default: 1.0)

Returns

Random number following Weibull distribution

Definition at line 1210 of file continuous_distributions.hpp.

weighted_covariance() [1/2]

template<typename Iterator1 , typename Iterator2 , typename WeightIterator >

double statcpp::weighted_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		WeightIterator	weight_first
	)

Weighted covariance.

Computes covariance with weights applied. Applies Bessel correction.

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
WeightIterator	Iterator type for weights

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
weight_first	Begin iterator for weights

Returns

Weighted covariance

Exceptions

std::invalid_argument

If range is empty, lengths differ, negative weight exists, or sum of weights is zero

Definition at line 925 of file correlation_covariance.hpp.

weighted_covariance() [2/2]

template<typename Iterator1 , typename Iterator2 , typename WeightIterator , typename Projection1 , typename Projection2 >

double statcpp::weighted_covariance	(	Iterator1	first1,
		Iterator1	last1,
		Iterator2	first2,
		Iterator2	last2,
		WeightIterator	weight_first,
		Projection1	proj1,
		Projection2	proj2
	)

Weighted covariance (projection version)

Template Parameters

Iterator1	Iterator type for the first data
Iterator2	Iterator type for the second data
WeightIterator	Iterator type for weights
Projection1	Projection function type for the first data
Projection2	Projection function type for the second data

Parameters

first1	Begin iterator for the first data
last1	End iterator for the first data
first2	Begin iterator for the second data
last2	End iterator for the second data
weight_first	Begin iterator for weights
proj1	Projection function for the first data
proj2	Projection function for the second data

Returns

Weighted covariance

Exceptions

std::invalid_argument

If range is empty, lengths differ, negative weight exists, or sum of weights is zero

Definition at line 1019 of file correlation_covariance.hpp.

weighted_harmonic_mean() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_harmonic_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first
	)

Weighted harmonic mean.

Computes the harmonic mean with weights applied to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights

Returns

Weighted harmonic mean

Exceptions

std::invalid_argument

If range is empty, if negative weight exists, if value is zero, or if sum of weights is zero

Deprecated:

Use weighted_harmonic_mean(first, last, weight_first, weight_last) overload for range safety

Definition at line 939 of file basic_statistics.hpp.

weighted_harmonic_mean() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_harmonic_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		Projection	proj
	)

Weighted harmonic mean (projection version)

Computes the weighted harmonic mean of the results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
proj	Projection function

Returns

Weighted harmonic mean of projected values

Exceptions

std::invalid_argument

If range is empty, if negative weight exists, if value is zero, or if sum of weights is zero

Deprecated:

Use weighted_harmonic_mean(first, last, weight_first, weight_last, proj) overload for range safety

Definition at line 1047 of file basic_statistics.hpp.

weighted_harmonic_mean() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_harmonic_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last
	)

Weighted harmonic mean (safe range version)

Computes the harmonic mean with weights applied to each element. Validates that data and weight ranges have the same size.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights

Returns

Weighted harmonic mean

Exceptions

std::invalid_argument

If range is empty, if ranges differ in size, if negative weight exists, if value is zero, or if sum of weights is zero

Definition at line 885 of file basic_statistics.hpp.

weighted_harmonic_mean() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_harmonic_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		Projection	proj
	)

Weighted harmonic mean (safe range version with projection)

Computes the weighted harmonic mean of the results after applying a projection function to each element. Validates that data and weight ranges have the same size.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights
proj	Projection function

Returns

Weighted harmonic mean of projected values

Exceptions

std::invalid_argument

If range is empty, if ranges differ in size, if negative weight exists, if value is zero, or if sum of weights is zero

Definition at line 991 of file basic_statistics.hpp.

weighted_mean() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first
	)

Definition at line 715 of file basic_statistics.hpp.

weighted_mean() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		Projection	proj
	)

Definition at line 796 of file basic_statistics.hpp.

weighted_mean() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last
	)

Weighted mean.

Computes the mean with weights applied to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights

Returns

Weighted mean

Exceptions

std::invalid_argument

If range is empty, if negative weight exists, or if sum of weights is zero

Definition at line 680 of file basic_statistics.hpp.

weighted_mean() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		Projection	proj
	)

Weighted mean (projection version)

Computes the weighted mean of the results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
proj	Projection function

Returns

Weighted mean of projected values

Exceptions

std::invalid_argument

If range is empty, if negative weight exists, or if sum of weights is zero

Definition at line 761 of file basic_statistics.hpp.

weighted_median() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_median	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first
	)

Weighted median.

Calculates the weighted median.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights

Returns

Weighted median

Exceptions

std::invalid_argument

If range is empty, weight is negative, or sum of weights is zero

Definition at line 493 of file order_statistics.hpp.

weighted_median() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_median	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		Projection	proj
	)

Weighted median with projection.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
proj	Projection function

Returns

Weighted median

Exceptions

std::invalid_argument

If range is empty, weight is negative, or sum of weights is zero

Definition at line 651 of file order_statistics.hpp.

weighted_median() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_median	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last
	)

Weighted median (safe overload)

Calculates the weighted median with range safety validation.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
weight_last	End of weights

Returns

Weighted median

Exceptions

std::invalid_argument

If range is empty, sizes mismatch, weight is negative, or sum of weights is zero

Definition at line 413 of file order_statistics.hpp.

weighted_median() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_median	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		Projection	proj
	)

Weighted median with projection (safe overload)

Calculates the weighted median with range safety validation.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
weight_last	End of weights
proj	Projection function

Returns

Weighted median

Exceptions

std::invalid_argument

If range is empty, sizes mismatch, weight is negative, or sum of weights is zero

Definition at line 571 of file order_statistics.hpp.

weighted_percentile() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_percentile	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		double	p
	)

Weighted percentile.

Calculates the weighted percentile.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
p	Percentile as proportion 0.0-1.0

Returns

Weighted percentile value

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 814 of file order_statistics.hpp.

weighted_percentile() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_percentile	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		double	p,
		Projection	proj
	)

Weighted percentile with projection.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
p	Percentile as proportion 0.0-1.0
proj	Projection function

Returns

Weighted percentile value

Exceptions

std::invalid_argument

If parameters are invalid

Definition at line 976 of file order_statistics.hpp.

weighted_percentile() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_percentile	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		double	p
	)

Weighted percentile (safe overload)

Calculates the weighted percentile with range safety validation.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
weight_last	End of weights
p	Percentile as proportion 0.0-1.0

Returns

Weighted percentile value

Exceptions

std::invalid_argument

If parameters are invalid or sizes mismatch

Definition at line 732 of file order_statistics.hpp.

weighted_percentile() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_percentile	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		double	p,
		Projection	proj
	)

Weighted percentile with projection (safe overload)

Calculates the weighted percentile with range safety validation.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Beginning of range
last	End of range
weight_first	Beginning of weights
weight_last	End of weights
p	Percentile as proportion 0.0-1.0
proj	Projection function

Returns

Weighted percentile value

Exceptions

std::invalid_argument

If parameters are invalid or sizes mismatch

Definition at line 894 of file order_statistics.hpp.

weighted_stddev() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_stddev	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first
	)

Weighted standard deviation.

Deprecated:

Use weighted_stddev(first, last, weight_first, weight_last) overload for range safety

Computes the square root of weighted variance.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights

Returns

Weighted standard deviation

Exceptions

std::invalid_argument

If range is empty, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1446 of file dispersion_spread.hpp.

weighted_stddev() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_stddev	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		Projection	proj
	)

Weighted standard deviation (projection version)

Deprecated:

Use weighted_stddev(first, last, weight_first, weight_last, proj) overload for range safety

Computes the weighted standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
proj	Projection function

Returns

Weighted standard deviation of projected values

Exceptions

std::invalid_argument

If range is empty, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1492 of file dispersion_spread.hpp.

weighted_stddev() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_stddev	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last
	)

Weighted standard deviation.

Computes the square root of weighted variance.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights

Returns

Weighted standard deviation

Exceptions

std::invalid_argument

If range is empty, data and weight ranges differ in length, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1424 of file dispersion_spread.hpp.

weighted_stddev() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_stddev	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		Projection	proj
	)

Weighted standard deviation (projection version)

Computes the weighted standard deviation of results after applying a projection function to each element.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights
proj	Projection function

Returns

Weighted standard deviation of projected values

Exceptions

std::invalid_argument

If range is empty, data and weight ranges differ in length, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1468 of file dispersion_spread.hpp.

weighted_variance() [1/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_variance	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first
	)

Weighted variance (reliability weights / analytic weights)

Deprecated:

Use weighted_variance(first, last, weight_first, weight_last) overload for range safety

Computes variance with weights applied to each element. Returns unbiased estimator with Bessel's correction.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights

Returns

Weighted variance

Exceptions

std::invalid_argument

If range is empty, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1206 of file dispersion_spread.hpp.

weighted_variance() [2/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_variance	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		Projection	proj
	)

Weighted variance (projection version)

Deprecated:

Use weighted_variance(first, last, weight_first, weight_last, proj) overload for range safety

Computes weighted variance of results after applying a projection function to each element. Returns unbiased estimator with Bessel's correction.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
proj	Projection function

Returns

Weighted variance of projected values

Exceptions

std::invalid_argument

If range is empty, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1356 of file dispersion_spread.hpp.

weighted_variance() [3/4]

template<typename Iterator , typename WeightIterator >

double statcpp::weighted_variance	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last
	)

Weighted variance (reliability weights / analytic weights)

Computes variance with weights applied to each element. Returns unbiased estimator with Bessel's correction.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights

Returns

Weighted variance

Exceptions

std::invalid_argument

If range is empty, data and weight ranges differ in length, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1129 of file dispersion_spread.hpp.

weighted_variance() [4/4]

template<typename Iterator , typename WeightIterator , typename Projection >

double statcpp::weighted_variance	(	Iterator	first,
		Iterator	last,
		WeightIterator	weight_first,
		WeightIterator	weight_last,
		Projection	proj
	)

Weighted variance (projection version)

Computes weighted variance of results after applying a projection function to each element. Returns unbiased estimator with Bessel's correction.

Template Parameters

Iterator	Iterator type
WeightIterator	Weight iterator type
Projection	Projection function type

Parameters

first	Begin iterator
last	End iterator
weight_first	Begin iterator for weights
weight_last	End iterator for weights
proj	Projection function

Returns

Weighted variance of projected values

Exceptions

std::invalid_argument

If range is empty, data and weight ranges differ in length, negative weights exist, sum of weights is zero, or insufficient effective sample size

Definition at line 1279 of file dispersion_spread.hpp.

wilcoxon_signed_rank_test()

template<typename Iterator >

test_result statcpp::wilcoxon_signed_rank_test	(	Iterator	first,
		Iterator	last,
		double	mu0 = 0.0,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

Perform Wilcoxon signed-rank test (one-sample)

Tests whether the median of data equals a specified value. A nonparametric test that does not assume normal distribution. Uses normal approximation (with continuity correction) for p-value calculation.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of range
last	Ending iterator of range
mu0	Median under null hypothesis (default: 0.0)
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result containing W+ statistic (sum of ranks for positive differences), p-value, and sample size of non-zero differences

Exceptions

std::invalid_argument	If there are fewer than 2 elements
std::invalid_argument	If there are fewer than 2 non-zero differences

Note

Null hypothesis: Median equals mu0

Observations with zero difference from mu0 are excluded

Definition at line 559 of file nonparametric_tests.hpp.

winsorize()

template<typename Iterator >

std::vector< double > statcpp::winsorize	(	Iterator	first,
		Iterator	last,
		double	limits = 0.05
	)

Winsorization.

Replaces extreme values with specified percentile values.

Template Parameters

Iterator

Iterator type

Parameters

first	Beginning of range
last	End of range
limits	Proportion to replace from each tail (e.g., 0.05 = replace top and bottom 5%)

Returns

Winsorized data

Exceptions

std::invalid_argument

If range is empty or limits is invalid

Note

Reduces the impact of outliers while preserving the number of data points.

Definition at line 303 of file robust.hpp.

z_test()

template<typename Iterator >

test_result statcpp::z_test	(	Iterator	first,
		Iterator	last,
		double	mu0,
		double	sigma,
		alternative_hypothesis	alt = alternative_hypothesis::two_sided
	)

One-sample z-test (known variance)

Tests whether the sample mean equals a specific value when the population variance is known.

Template Parameters

Iterator

Input iterator type

Parameters

first	Beginning iterator of sample data
last	End iterator of sample data
mu0	Population mean under null hypothesis
sigma	Known population standard deviation
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (z-statistic, p-value, df=infinity)

Exceptions

std::invalid_argument

If sigma is not positive or range is empty

Definition at line 72 of file parametric_tests.hpp.

z_test_proportion()

test_result statcpp::z_test_proportion ( std::size_t  successes, std::size_t  trials, double  p0, alternative_hypothesis  alt = alternative_hypothesis::two_sided  )

inline

One-sample proportion z-test.

Tests whether the sample proportion equals a specific population proportion.

Parameters

successes	Number of successes
trials	Number of trials
p0	Population proportion under null hypothesis
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (z-statistic, p-value, df=infinity)

Exceptions

std::invalid_argument

If p0 is outside (0,1), trials is 0, or successes exceeds trials

Definition at line 121 of file parametric_tests.hpp.

z_test_proportion_two_sample()

test_result statcpp::z_test_proportion_two_sample ( std::size_t  successes1, std::size_t  trials1, std::size_t  successes2, std::size_t  trials2, alternative_hypothesis  alt = alternative_hypothesis::two_sided  )

inline

Two-sample proportion z-test.

Tests whether two sample proportions are equal (using pooled proportion).

Parameters

successes1	Number of successes in first sample
trials1	Number of trials in first sample
successes2	Number of successes in second sample
trials2	Number of trials in second sample
alt	Type of alternative hypothesis (default: two-sided)

Returns

test_result Test result (z-statistic, p-value, df=infinity)

Exceptions

std::invalid_argument

If trials is 0 or successes exceeds trials

Definition at line 169 of file parametric_tests.hpp.

Variable Documentation

default_abs_tol

constexpr double statcpp::default_abs_tol = 1e-12

constexpr

Default absolute tolerance for floating-point comparisons.

Definition at line 29 of file numerical_utils.hpp.

default_rel_tol

constexpr double statcpp::default_rel_tol = 1e-9

constexpr

Default relative tolerance for floating-point comparisons.

Definition at line 24 of file numerical_utils.hpp.

epsilon

constexpr double statcpp::epsilon = std::numeric_limits<double>::epsilon()

constexpr

Machine epsilon for double precision.

Definition at line 19 of file numerical_utils.hpp.

is_random_engine_v

template<typename T >

constexpr bool statcpp::is_random_engine_v = is_random_engine<T>::value

inlineconstexpr

Variable template version of is_random_engine.

Template Parameters

T	Type to check

Definition at line 131 of file random_engine.hpp.

log_sqrt_2_pi

constexpr double statcpp::log_sqrt_2_pi = 0.91893853320467274178

inlineconstexpr

Natural logarithm of sqrt(2*pi)

Definition at line 39 of file special_functions.hpp.

NA

constexpr double statcpp::NA = std::numeric_limits<double>::quiet_NaN()

inlineconstexpr

Constant representing NA (NaN)

Definition at line 38 of file data_wrangling.hpp.

pi

constexpr double statcpp::pi = 3.14159265358979323846

inlineconstexpr

Pi constant.

Definition at line 24 of file special_functions.hpp.

sqrt_2

constexpr double statcpp::sqrt_2 = 1.41421356237309504880

inlineconstexpr

Square root of 2.

Definition at line 29 of file special_functions.hpp.

sqrt_2_pi

constexpr double statcpp::sqrt_2_pi = 2.50662827463100050242

inlineconstexpr

Square root of 2*pi.

Definition at line 34 of file special_functions.hpp.