Class providing methods for computing cumulative distribution functions (CDFs) More...

#include <cdfs.hpp>

Static Public Member Functions
static double	bernoulli (double x, double p)
	Compute the cumulative distribution function (CDF) of the Bernoulli distribution. More...

static double	beta (double x, double alpha, double beta)
	Compute the cumulative distribution function (CDF) of the beta distribution. More...

static double	binomial (int k, int n, double p)
	Compute the cumulative distribution function (CDF) of the binomial distribution. More...

static double	cauchy (double x, double x0, double gamma)
	Compute the cumulative distribution function (CDF) of the Cauchy distribution. More...

static double	chi_squared (double x, double k)
	Compute the cumulative distribution function (CDF) of the chi-squared distribution. More...

static double	exponential (double x, double lambda)
	Compute the cumulative distribution function (CDF) of the exponential distribution. More...

static double	f (double x, double df1, double df2)
	Compute the cumulative distribution function (CDF) of the F distribution. More...

static double	gamma (double x, double shape, double scale)
	Compute the cumulative distribution function (CDF) of the gamma distribution. More...

static double	inverse_gamma (double x, double shape, double scale)
	Compute the cumulative distribution function (CDF) of the inverse-gamma distribution. More...

static double	inverse_gaussian (double x, double mu, double lambda)
	Compute the cumulative distribution function (CDF) of the inverse-Gaussian distribution. More...

static double	laplace (double x, double mu, double b)
	Compute the cumulative distribution function (CDF) of the Laplace distribution. More...

static double	logistic (double x, double mu, double s)
	Compute the cumulative distribution function (CDF) of the logistic distribution. More...

static double	log_normal (double x, double mu, double sigma)
	Compute the cumulative distribution function (CDF) of the log-normal distribution. More...

static double	gaussian (double x, double mu, double sigma)
	Compute the cumulative distribution function (CDF) of the normal (Gaussian) distribution. More...

static double	poisson (int k, double lambda)
	Compute the cumulative distribution function (CDF) of the Poisson distribution. More...

static double	rademacher (double x)
	Compute the cumulative distribution function (CDF) of the Rademacher distribution. More...

static double	student_t (double x, double df)
	Compute the cumulative distribution function (CDF) of Student's t distribution. More...

static double	uniform (double x, double a, double b)
	Compute the cumulative distribution function (CDF) of the uniform distribution. More...

static double	weibull (double x, double shape, double scale)
	Compute the cumulative distribution function (CDF) of the Weibull distribution. More...

static double	normal_cdf (double x)
	Compute the cumulative distribution function (CDF) of the standard normal distribution. More...

static double	incomplete_beta (double a, double b, double x)
	Compute the incomplete beta function. More...

static double	incomplete_gamma (double a, double x)
	Compute the incomplete gamma function. More...

Detailed Description

Class providing methods for computing cumulative distribution functions (CDFs)

Definition at line 43 of file cdfs.hpp.

Member Function Documentation

◆ bernoulli()

double gpmp::stats::CDF::bernoulli	(	double	x,
		double	p
	)

static

Compute the cumulative distribution function (CDF) of the Bernoulli distribution.

Parameters

x	The value at which to evaluate the CDF
p	The probability parameter of the Bernoulli distribution

Returns: The CDF value at the given point

Definition at line 43 of file cdfs.cpp.

                                                  {
     if (x < 0)
         return 0.0;
     else if (x < 1)
         return 1 - (1 - p);
     else
         return 1.0;
 }

Referenced by main().

◆ beta()

double gpmp::stats::CDF::beta	(	double	x,
		double	alpha,
		double	beta
	)

static

Compute the cumulative distribution function (CDF) of the beta distribution.

Parameters

x	The value at which to evaluate the CDF
alpha	The alpha parameter of the beta distribution
beta	The beta parameter of the beta distribution

Returns: The CDF value at the given point

Definition at line 53 of file cdfs.cpp.

                                                              {
     if (x <= 0)
         return 0.0;
     else if (x >= 1)
         return 1.0;
     else
         return incomplete_beta(alpha, beta, x);
 }

Referenced by main().

◆ binomial()

double gpmp::stats::CDF::binomial	(	int	k,
		int	n,
		double	p
	)

static

Compute the cumulative distribution function (CDF) of the binomial distribution.

Parameters

k	The number of successes
n	The number of trials
p	The probability of success in each trial

Returns: The CDF value at the given point

Definition at line 63 of file cdfs.cpp.

                                                     {
     if (k < 0)
         return 0.0;
     else if (k >= n)
         return 1.0;
     else
         return incomplete_beta(1.0 - p, n - k, k + 1);
 }

Referenced by main().

◆ cauchy()

double gpmp::stats::CDF::cauchy	(	double	x,
		double	x0,
		double	gamma
	)

static

Compute the cumulative distribution function (CDF) of the Cauchy distribution.

Parameters

x	The value at which to evaluate the CDF
x0	The location parameter of the Cauchy distribution
gamma	The scale parameter of the Cauchy distribution

Returns: The CDF value at the given point

Definition at line 73 of file cdfs.cpp.

                                                              {
     return 0.5 + atan((x - x0) / gamma) / M_PI;
 }

Referenced by main().

◆ chi_squared()

double gpmp::stats::CDF::chi_squared	(	double	x,
		double	k
	)

static

Compute the cumulative distribution function (CDF) of the chi-squared distribution.

Parameters

x	The value at which to evaluate the CDF
k	The degrees of freedom parameter of the chi-squared distribution

Returns: The CDF value at the given point

Definition at line 78 of file cdfs.cpp.

                                                    {
     if (x < 0)
         return 0.0;
     else
         return incomplete_gamma(k / 2.0, x / 2.0);
 }

Referenced by main().

◆ exponential()

double gpmp::stats::CDF::exponential	(	double	x,
		double	lambda
	)

static

Compute the cumulative distribution function (CDF) of the exponential distribution.

Parameters

x	The value at which to evaluate the CDF
lambda	The rate parameter of the exponential distribution

Returns: The CDF value at the given point

Definition at line 86 of file cdfs.cpp.

                                                         {
     if (x < 0)
         return 0.0;
     else
         return 1.0 - exp(-lambda * x);
 }

Referenced by main().

◆ f()

double gpmp::stats::CDF::f	(	double	x,
		double	df1,
		double	df2
	)

static

Compute the cumulative distribution function (CDF) of the F distribution.

Parameters

x	The value at which to evaluate the CDF
df1	The numerator degrees of freedom parameter of the F distribution
df2	The denominator degrees of freedom parameter of the F distribution

Returns: The CDF value at the given point

Definition at line 94 of file cdfs.cpp.

                                                        {
     if (x <= 0)
         return 0.0;
     else
         return incomplete_beta(df1 / 2.0, df2 / 2.0, df1 / (df1 + df2 * x));
 }

Referenced by main().

◆ gamma()

double gpmp::stats::CDF::gamma	(	double	x,
		double	shape,
		double	scale
	)

static

Compute the cumulative distribution function (CDF) of the gamma distribution.

Parameters

x	The value at which to evaluate the CDF
shape	The shape parameter of the gamma distribution
scale	The scale parameter of the gamma distribution

Returns: The CDF value at the given point

Definition at line 102 of file cdfs.cpp.

                                                                {
     if (x < 0)
         return 0.0;
     else
         return incomplete_gamma(shape, x / scale);
 }

Referenced by main().

◆ gaussian()

double gpmp::stats::CDF::gaussian	(	double	x,
		double	mu,
		double	sigma
	)

static

Compute the cumulative distribution function (CDF) of the normal (Gaussian) distribution.

Parameters

x	The value at which to evaluate the CDF
mu	The mean parameter of the normal distribution
sigma	The standard deviation parameter of the normal distribution

Returns: The CDF value at the given point

Definition at line 147 of file cdfs.cpp.

                                                                {
     return 0.5 * (1 + erf((x - mu) / (sigma * sqrt(2))));
 }

Referenced by main().

◆ incomplete_beta()

double gpmp::stats::CDF::incomplete_beta	(	double	a,
		double	b,
		double	x
	)

static

Compute the incomplete beta function.

Parameters

a	The first parameter of the incomplete beta function
b	The second parameter of the incomplete beta function
x	The value at which to evaluate the incomplete beta function

Returns: The value of the incomplete beta function at the given point

Definition at line 201 of file cdfs.cpp.

                                                                  {
     const int maxIterations = 1000;
     const double epsilon = 1e-12;
     double result = 0.0;
     double term = 1.0;
     for (int k = 0; k < maxIterations; ++k) {
         term *=
             (k == 0 ? 1.0
                     : (a + k - 1) * (b - k) / (a + b + k - 1) * x / (k + 1));
         result += term;
         if (std::abs(term) < epsilon * std::abs(result))
             break;
     }
     return result * std::pow(x, a) * std::pow(1 - x, b) / (a * std::beta(a, b));
 }

◆ incomplete_gamma()

double gpmp::stats::CDF::incomplete_gamma	(	double	a,
		double	x
	)

static

Compute the incomplete gamma function.

Parameters

a	The shape parameter of the incomplete gamma function
x	The value at which to evaluate the incomplete gamma function

Returns: The value of the incomplete gamma function at the given point

Definition at line 218 of file cdfs.cpp.

                                                         {
     const int maxIterations = 1000;
     const double epsilon = 1e-12;
     double result = 0.0;
     double term = 1.0;
     for (int k = 0; k < maxIterations; ++k) {
         term *= x / (a + k);
         result += term;
         if (std::abs(term) < epsilon * std::abs(result))
             break;
     }
     return exp(-x) * std::pow(x, a) * result / std::tgamma(a);
 }

◆ inverse_gamma()

double gpmp::stats::CDF::inverse_gamma	(	double	x,
		double	shape,
		double	scale
	)

static

Compute the cumulative distribution function (CDF) of the inverse-gamma distribution.

Parameters

x	The value at which to evaluate the CDF
shape	The shape parameter of the inverse-gamma distribution
scale	The scale parameter of the inverse-gamma distribution

Returns: The CDF value at the given point

Definition at line 110 of file cdfs.cpp.

                                                                        {
     if (x <= 0)
         return 0.0;
     else
         return 1.0 - incomplete_gamma(shape, scale / x);
 }

Referenced by main().

◆ inverse_gaussian()

double gpmp::stats::CDF::inverse_gaussian	(	double	x,
		double	mu,
		double	lambda
	)

static

Compute the cumulative distribution function (CDF) of the inverse-Gaussian distribution.

Parameters

x	The value at which to evaluate the CDF
mu	The mean parameter of the inverse-Gaussian distribution
lambda	The shape parameter of the inverse-Gaussian distribution

Returns: The CDF value at the given point

Definition at line 118 of file cdfs.cpp.

                                                                         {
     if (x <= 0)
         return 0.0;
     else
         return normal_cdf(sqrt(lambda / x) * (x / mu - 1.0));
 }

Referenced by main().

◆ laplace()

double gpmp::stats::CDF::laplace	(	double	x,
		double	mu,
		double	b
	)

static

Compute the cumulative distribution function (CDF) of the Laplace distribution.

Parameters

x	The value at which to evaluate the CDF
mu	The location parameter of the Laplace distribution
b	The scale parameter of the Laplace distribution

Returns: The CDF value at the given point

Definition at line 126 of file cdfs.cpp.

                                                           {
     if (x < mu)
         return 0.5 * exp((x - mu) / b);
     else
         return 1.0 - 0.5 * exp(-(x - mu) / b);
 }

Referenced by main().

◆ log_normal()

double gpmp::stats::CDF::log_normal	(	double	x,
		double	mu,
		double	sigma
	)

static

Compute the cumulative distribution function (CDF) of the log-normal distribution.

Parameters

x	The value at which to evaluate the CDF
mu	The mean parameter of the log-normal distribution
sigma	The standard deviation parameter of the log-normal distribution

Returns: The CDF value at the given point

Definition at line 139 of file cdfs.cpp.

                                                                  {
     if (x <= 0)
         return 0.0;
     else
         return 0.5 + 0.5 * erf((log(x) - mu) / (sqrt(2.0) * sigma));
 }

Referenced by main().

◆ logistic()

double gpmp::stats::CDF::logistic	(	double	x,
		double	mu,
		double	s
	)

static

Compute the cumulative distribution function (CDF) of the logistic distribution.

Parameters

x	The value at which to evaluate the CDF
mu	The location parameter of the logistic distribution
s	The scale parameter of the logistic distribution

Returns: The CDF value at the given point

Definition at line 134 of file cdfs.cpp.

                                                            {
     return 1.0 / (1.0 + exp(-(x - mu) / s));
 }

Referenced by main().

◆ normal_cdf()

double gpmp::stats::CDF::normal_cdf ( double x )

static

Compute the cumulative distribution function (CDF) of the standard normal distribution.

Parameters

x	The value at which to evaluate the CDF

Returns: The CDF value at the given point

Definition at line 196 of file cdfs.cpp.

                                         {
     return 0.5 * (1 + erf(x / sqrt(2.0)));
 }

◆ poisson()

double gpmp::stats::CDF::poisson	(	int	k,
		double	lambda
	)

static

Compute the cumulative distribution function (CDF) of the Poisson distribution.

Parameters

k	The number of occurrences
lambda	The rate parameter of the Poisson distribution

Returns: The CDF value at the given point

Definition at line 152 of file cdfs.cpp.

                                                  {
     if (k < 0)
         return 0.0;
     else
         return incomplete_gamma(k + 1, lambda);
 }

Referenced by main().

◆ rademacher()

double gpmp::stats::CDF::rademacher ( double x )

static

Compute the cumulative distribution function (CDF) of the Rademacher distribution.

Parameters

x	The value at which to evaluate the CDF

Returns: The CDF value at the given point

Definition at line 160 of file cdfs.cpp.

                                         {
     if (x < 0)
         return 0.0;
     else if (x < 0.5)
         return 0.0;
     else
         return 1.0;
 }

Referenced by main().

◆ student_t()

double gpmp::stats::CDF::student_t	(	double	x,
		double	df
	)

static

Compute the cumulative distribution function (CDF) of Student's t distribution.

Parameters

x	The value at which to evaluate the CDF
df	The degrees of freedom parameter of Student's t distribution

Returns: The CDF value at the given point

Definition at line 170 of file cdfs.cpp.

                                                   {
     if (df <= 0)
         return NAN;
     return 0.5 + 0.5 * std::tgamma((df + 1) / 2) * std::hypot(1, x / sqrt(df)) /
                      (sqrt(df) * std::tgamma(df / 2));
 }

Referenced by main().

◆ uniform()

double gpmp::stats::CDF::uniform	(	double	x,
		double	a,
		double	b
	)

static

Compute the cumulative distribution function (CDF) of the uniform distribution.

Parameters

x	The value at which to evaluate the CDF
a	The minimum value of the uniform distribution
b	The maximum value of the uniform distribution

Returns: The CDF value at the given point

Definition at line 178 of file cdfs.cpp.

                                                          {
     if (x < a)
         return 0.0;
     else if (x < b)
         return (x - a) / (b - a);
     else
         return 1.0;
 }

Referenced by main().

◆ weibull()

double gpmp::stats::CDF::weibull	(	double	x,
		double	shape,
		double	scale
	)

static

Compute the cumulative distribution function (CDF) of the Weibull distribution.

Parameters

x	The value at which to evaluate the CDF
shape	The shape parameter of the Weibull distribution
scale	The scale parameter of the Weibull distribution

Returns: The CDF value at the given point

Definition at line 188 of file cdfs.cpp.

                                                                  {
     if (x < 0)
         return 0.0;
     else
         return 1.0 - exp(-pow(x / scale, shape));
 }

Referenced by main().

The documentation for this class was generated from the following files:

include/openGPMP/stats/cdfs.hpp
modules/stats/cdfs.cpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ bernoulli()

◆ beta()

◆ binomial()

◆ cauchy()

◆ chi_squared()

◆ exponential()

◆ f()

◆ gamma()

◆ gaussian()

◆ incomplete_beta()

◆ incomplete_gamma()

◆ inverse_gamma()

◆ inverse_gaussian()

◆ laplace()

◆ log_normal()

◆ logistic()

◆ normal_cdf()

◆ poisson()

◆ rademacher()

◆ student_t()

◆ uniform()

◆ weibull()