continuous_distributions.hpp File Reference

Continuous distribution functions. More...

#include "statcpp/special_functions.hpp"
#include "statcpp/random_engine.hpp"
#include <algorithm>
#include <cmath>
#include <limits>
#include <random>
#include <stdexcept>

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Namespaces
namespace	statcpp

Functions
double	statcpp::uniform_pdf (double x, double a=0.0, double b=1.0)
	Uniform distribution probability density function (PDF)
double	statcpp::uniform_cdf (double x, double a=0.0, double b=1.0)
	Uniform distribution cumulative distribution function (CDF)
double	statcpp::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	statcpp::uniform_rand (double a, double b, Engine &engine)
	Uniform distribution random number generation.
double	statcpp::uniform_rand (double a=0.0, double b=1.0)
	Uniform distribution random number generation (using default engine)
double	statcpp::normal_pdf (double x, double mu=0.0, double sigma=1.0)
	Normal distribution probability density function (PDF)
double	statcpp::normal_cdf (double x, double mu=0.0, double sigma=1.0)
	Normal distribution cumulative distribution function (CDF)
double	statcpp::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	statcpp::normal_rand (double mu, double sigma, Engine &engine)
	Normal distribution random number generation.
double	statcpp::normal_rand (double mu=0.0, double sigma=1.0)
	Normal distribution random number generation (using default engine)
double	statcpp::exponential_pdf (double x, double lambda=1.0)
	Exponential distribution probability density function (PDF)
double	statcpp::exponential_cdf (double x, double lambda=1.0)
	Exponential distribution cumulative distribution function (CDF)
double	statcpp::exponential_quantile (double p, double lambda=1.0)
	Exponential distribution quantile function.
template<typename Engine = default_random_engine>
double	statcpp::exponential_rand (double lambda, Engine &engine)
	Exponential distribution random number generation.
double	statcpp::exponential_rand (double lambda=1.0)
	Exponential distribution random number generation (using default engine)
double	statcpp::gamma_pdf (double x, double shape, double rate=1.0)
	Gamma distribution probability density function (PDF)
double	statcpp::gamma_cdf (double x, double shape, double rate=1.0)
	Gamma distribution cumulative distribution function (CDF)
double	statcpp::gamma_quantile (double p, double shape, double rate=1.0)
	Gamma distribution quantile function.
template<typename Engine = default_random_engine>
double	statcpp::gamma_rand (double shape, double rate, Engine &engine)
	Gamma distribution random number generation.
double	statcpp::gamma_rand (double shape, double rate=1.0)
	Gamma distribution random number generation (using default engine)
double	statcpp::beta_pdf (double x, double alpha, double beta_param)
	Beta distribution probability density function (PDF)
double	statcpp::beta_cdf (double x, double alpha, double beta_param)
	Beta distribution cumulative distribution function (CDF)
double	statcpp::beta_quantile (double p, double alpha, double beta_param)
	Beta distribution quantile function.
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)
double	statcpp::beta_rand (double alpha, double beta_param)
	Beta distribution random number generation (using default engine)
double	statcpp::chisq_pdf (double x, double df)
	Chi-square distribution probability density function (PDF)
double	statcpp::chisq_cdf (double x, double df)
	Chi-square distribution cumulative distribution function (CDF)
double	statcpp::chisq_quantile (double p, double df)
	Chi-square distribution quantile function.
template<typename Engine = default_random_engine>
double	statcpp::chisq_rand (double df, Engine &engine)
	Chi-square distribution random number generation.
double	statcpp::chisq_rand (double df)
	Chi-square distribution random number generation (using default engine)
double	statcpp::t_pdf (double x, double df)
	t-distribution probability density function (PDF)
double	statcpp::t_cdf (double x, double df)
	t-distribution cumulative distribution function (CDF)
double	statcpp::t_quantile (double p, double df)
	t-distribution quantile function (Newton-Raphson method)
template<typename Engine = default_random_engine>
double	statcpp::t_rand (double df, Engine &engine)
	t-distribution random number generation
double	statcpp::t_rand (double df)
	t-distribution random number generation (using default engine)
double	statcpp::f_pdf (double x, double df1, double df2)
	F-distribution probability density function (PDF)
double	statcpp::f_cdf (double x, double df1, double df2)
	F-distribution cumulative distribution function (CDF)
double	statcpp::f_quantile (double p, double df1, double df2)
	F-distribution quantile function (Newton-Raphson method)
template<typename Engine = default_random_engine>
double	statcpp::f_rand (double df1, double df2, Engine &engine)
	F-distribution random number generation.
double	statcpp::f_rand (double df1, double df2)
	F-distribution random number generation (using default engine)
double	statcpp::lognormal_pdf (double x, double mu=0.0, double sigma=1.0)
	Log-normal distribution probability density function (PDF)
double	statcpp::lognormal_cdf (double x, double mu=0.0, double sigma=1.0)
	Log-normal distribution cumulative distribution function (CDF)
double	statcpp::lognormal_quantile (double p, double mu=0.0, double sigma=1.0)
	Log-normal distribution quantile function.
template<typename Engine = default_random_engine>
double	statcpp::lognormal_rand (double mu, double sigma, Engine &engine)
	Log-normal distribution random number generation.
double	statcpp::lognormal_rand (double mu=0.0, double sigma=1.0)
	Log-normal distribution random number generation (using default engine)
double	statcpp::weibull_pdf (double x, double shape, double scale=1.0)
	Weibull distribution probability density function (PDF)
double	statcpp::weibull_cdf (double x, double shape, double scale=1.0)
	Weibull distribution cumulative distribution function (CDF)
double	statcpp::weibull_quantile (double p, double shape, double scale=1.0)
	Weibull distribution quantile function.
template<typename Engine = default_random_engine>
double	statcpp::weibull_rand (double shape, double scale, Engine &engine)
	Weibull distribution random number generation.
double	statcpp::weibull_rand (double shape, double scale=1.0)
	Weibull distribution random number generation (using default engine)
double	statcpp::studentized_range_cdf (double q, double k, double df)
	CDF of the studentized range distribution.
double	statcpp::studentized_range_quantile (double p, double k, double df)
	Quantile function of the studentized range distribution.

Detailed Description

Continuous distribution functions.

Provides PDF, CDF, quantile, and random number generation functions for uniform, normal, exponential, gamma, beta, chi-square, t, F, log-normal, and Weibull distributions.

Definition in file continuous_distributions.hpp.