Class representing Probability Distribution Functions (PDFs) More...

#include <pdfs.hpp>

Static Public Member Functions
static double	bernoulli (double x, double p)
	Calculates the probability of success in a Bernoulli trial. More...

static double	beta (double x, double alpha, double beta)
	Calculates the probability density function (PDF) of the Beta distribution. More...

static double	binomial (int k, int n, double p)
	Calculates the probability of observing k successes in n independent Bernoulli trials. More...

static double	cauchy (double x, double x0, double gamma)
	Calculates the probability density function (PDF) of the Cauchy distribution. More...

static double	chi_squared (double x, int k)
	Calculates the probability density function (PDF) of the chi-squared distribution. More...

static double	exponential (double x, double lambda)
	Calculates the probability density function (PDF) of the exponential distribution. More...

static double	f_dist (double x, int df1, int df2)
	Calculates the probability density function (PDF) of the F distribution. More...

static double	gamma (double x, double alpha, double beta)
	Calculates the probability density function (PDF) of the gamma distribution. More...

static double	inverse_gamma (double x, double alpha, double beta)
	Calculates the probability density function (PDF) of the inverse gamma distribution. More...

static double	inverse_gaussian (double x, double mu, double lambda)
	Calculates the probability density function (PDF) of the inverse Gaussian distribution. More...

static double	laplace (double x, double mu, double b)
	Calculates the probability density function (PDF) of the Laplace distribution. More...

static double	logistic (double x, double mu, double s)
	Calculates the probability density function (PDF) of the logistic distribution. More...

static double	log_normal (double x, double mu, double sigma)
	Calculates the probability density function (PDF) of the log-normal distribution. More...

static double	gaussian (double x, double mu, double sigma)
	Calculates the probability density function (PDF) of the Gaussian (normal) distribution. More...

static double	poisson (int k, double lambda)
	Calculates the probability density function (PDF) of the Poisson distribution. More...

static double	rademacher (int k)
	Calculates the probability density function (PDF) of the Rademacher distribution. More...

static double	student_t (double x, int df)
	Calculates the probability density function (PDF) of Student's t distribution. More...

static double	uniform (double x, double a, double b)
	Calculates the probability density function (PDF) of the uniform distribution. More...

static double	weibull (double x, double k, double lambda)
	Calculates the probability density function (PDF) of the Weibull distribution. More...

static double	binomial_coefficient (int n, int k)
	Calculates the binomial coefficient "n choose k". More...

static double	beta_function (double alpha, double beta)
	Calculates the beta function. More...

static double	factorial (int n)
	Calculates the factorial of an integer. More...

Detailed Description

Class representing Probability Distribution Functions (PDFs)

Definition at line 41 of file pdfs.hpp.

Member Function Documentation

◆ bernoulli()

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

static

Calculates the probability of success in a Bernoulli trial.

Parameters

x	The outcome (0 or 1)
p	The probability of success

Returns: The probability of observing the outcome

Definition at line 44 of file pdfs.cpp.

                                                  {
     if (std::abs(x - 0) < std::numeric_limits<double>::epsilon())
         return 1 - p;
     else if (std::abs(x - 1) < std::numeric_limits<double>::epsilon())
         return p;
     else
         return 0;
 }

Referenced by main().

◆ beta()

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

static

Calculates the probability density function (PDF) of the Beta distribution.

Parameters

x	The value at which to evaluate the PDF
alpha	The shape parameter alpha (> 0)
beta	The shape parameter beta (> 0)

Returns: The value of the PDF at x

Definition at line 54 of file pdfs.cpp.

                                                              {
     if (x < 0 || x > 1)
         return 0;
     else
         return (std::pow(x, alpha - 1) * std::pow(1 - x, beta - 1)) /
                beta_function(alpha, beta);
 }

Referenced by main().

◆ beta_function()

double gpmp::stats::PDF::beta_function	(	double	alpha,
		double	beta
	)

static

Calculates the beta function.

Parameters

alpha	The first shape parameter (> 0)
beta	The second shape parameter (> 0)

Returns: The value of the beta function

Definition at line 212 of file pdfs.cpp.

                                                             {
     return std::tgamma(alpha) * std::tgamma(beta) / std::tgamma(alpha + beta);
 }

◆ binomial()

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

static

Calculates the probability of observing k successes in n independent Bernoulli trials.

Parameters

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

Returns: The probability of observing k successes

Definition at line 63 of file pdfs.cpp.

                                                     {
     if (k < 0 || k > n)
         return 0;
     else
         return binomial_coefficient(n, k) * std::pow(p, k) *
                std::pow(1 - p, n - k);
 }

Referenced by main().

◆ binomial_coefficient()

double gpmp::stats::PDF::binomial_coefficient	(	int	n,
		int	k
	)

static

Calculates the binomial coefficient "n choose k".

Parameters

n	The total number of items
k	The number of items to choose

Returns: The binomial coefficient

Definition at line 203 of file pdfs.cpp.

                                                       {
     double result = 1.0;
     for (int i = 1; i <= k; ++i) {
         result *= static_cast<double>(n - (k - i)) / i;
     }
     return result;
 }

◆ cauchy()

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

static

Calculates the probability density function (PDF) of the Cauchy distribution.

Parameters

x	The value at which to evaluate the PDF
x0	The location parameter
gamma	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 72 of file pdfs.cpp.

                                                              {
     return (1 / (M_PI * gamma)) *
            (gamma * gamma / ((x - x0) * (x - x0) + gamma * gamma));
 }

Referenced by main().

◆ chi_squared()

double gpmp::stats::PDF::chi_squared	(	double	x,
		int	k
	)

static

Calculates the probability density function (PDF) of the chi-squared distribution.

Parameters

x	The value at which to evaluate the PDF
k	The degrees of freedom (> 0)

Returns: The value of the PDF at x

Definition at line 78 of file pdfs.cpp.

                                                 {
     if (x < 0)
         return 0;
     else
         return (std::pow(x, k / 2.0 - 1) * std::exp(-x / 2.0)) /
                (std::pow(2, k / 2.0) * std::tgamma(k / 2.0));
 }

Referenced by main().

◆ exponential()

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

static

Calculates the probability density function (PDF) of the exponential distribution.

Parameters

x	The value at which to evaluate the PDF
lambda	The rate parameter (> 0)

Returns: The value of the PDF at x

Definition at line 87 of file pdfs.cpp.

                                                         {
     if (x < 0)
         return 0;
     else
         return lambda * std::exp(-lambda * x);
 }

Referenced by main().

◆ f_dist()

double gpmp::stats::PDF::f_dist	(	double	x,
		int	df1,
		int	df2
	)

static

Calculates the probability density function (PDF) of the F distribution.

Parameters

x	The value at which to evaluate the PDF
df1	The degrees of freedom of the numerator (> 0)
df2	The degrees of freedom of the denominator (> 0)

Returns: The value of the PDF at x

Definition at line 95 of file pdfs.cpp.

                                                       {
     if (x < 0)
         return 0;
     else
         return std::pow(df1, df1 / 2.0) * std::pow(df2, df2 / 2.0) *
                std::pow(x, df1 / 2.0 - 1) /
                (std::pow(df2 + df1 * x, (df1 + df2) / 2.0) *
                 std::tgamma(df1 / 2.0) * std::tgamma(df2 / 2.0));
 }

Referenced by main().

◆ factorial()

static double gpmp::stats::PDF::factorial ( int n )

static

Calculates the factorial of an integer.

Parameters

n	The integer

Returns: The factorial of n

◆ gamma()

double gpmp::stats::PDF::gamma	(	double	x,
		double	alpha,
		double	beta
	)

static

Calculates the probability density function (PDF) of the gamma distribution.

Parameters

x	The value at which to evaluate the PDF
alpha	The shape parameter (> 0)
beta	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 106 of file pdfs.cpp.

                                                               {
     if (x < 0)
         return 0;
     else
         return (std::pow(x, alpha - 1) * std::exp(-x / beta)) /
                (std::pow(beta, alpha) * std::tgamma(alpha));
 }

Referenced by main().

◆ gaussian()

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

static

Calculates the probability density function (PDF) of the Gaussian (normal) distribution.

Parameters

x	The value at which to evaluate the PDF
mu	The mean of the distribution
sigma	The standard deviation of the distribution (> 0)

Returns: The value of the PDF at x

Definition at line 154 of file pdfs.cpp.

                                                                {
     return (1 / (sigma * std::sqrt(2 * M_PI))) *
            std::exp(-0.5 * std::pow((x - mu) / sigma, 2));
 }

Referenced by main().

◆ inverse_gamma()

double gpmp::stats::PDF::inverse_gamma	(	double	x,
		double	alpha,
		double	beta
	)

static

Calculates the probability density function (PDF) of the inverse gamma distribution.

Parameters

x	The value at which to evaluate the PDF
alpha	The shape parameter (> 0)
beta	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 115 of file pdfs.cpp.

                                                                       {
     if (x <= 0)
         return 0;
     else
         return (std::pow(beta, alpha) * std::pow(x, -alpha - 1) *
                 std::exp(-beta / x)) /
                std::tgamma(alpha);
 }

Referenced by main().

◆ inverse_gaussian()

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

static

Calculates the probability density function (PDF) of the inverse Gaussian distribution.

Parameters

x	The value at which to evaluate the PDF
mu	The mean parameter (> 0)
lambda	The shape parameter (> 0)

Returns: The value of the PDF at x

Definition at line 125 of file pdfs.cpp.

                                                                         {
     if (x <= 0)
         return 0;
     else
         return std::sqrt(lambda / (2 * M_PI * x * x * x)) *
                std::exp(-lambda * (x - mu) * (x - mu) / (2 * mu * mu * x));
 }

Referenced by main().

◆ laplace()

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

static

Calculates the probability density function (PDF) of the Laplace distribution.

Parameters

x	The value at which to evaluate the PDF
mu	The location parameter
b	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 134 of file pdfs.cpp.

                                                           {
     return 0.5 * std::exp(-std::abs(x - mu) / b) / b;
 }

Referenced by main().

◆ log_normal()

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

static

Calculates the probability density function (PDF) of the log-normal distribution.

Parameters

x	The value at which to evaluate the PDF
mu	The mean of the underlying normal distribution
sigma	The standard deviation of the underlying normal distribution (> 0)

Returns: The value of the PDF at x

Definition at line 145 of file pdfs.cpp.

                                                                  {
     if (x <= 0)
         return 0;
     else
         return (1 / (x * sigma * std::sqrt(2 * M_PI))) *
                std::exp(-0.5 * std::pow((std::log(x) - mu) / sigma, 2));
 }

Referenced by main().

◆ logistic()

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

static

Calculates the probability density function (PDF) of the logistic distribution.

Parameters

x	The value at which to evaluate the PDF
mu	The location parameter
s	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 139 of file pdfs.cpp.

                                                            {
     double z = (x - mu) / s;
     return std::exp(-z) / (s * std::pow(1 + std::exp(-z), 2));
 }

Referenced by main().

◆ poisson()

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

static

Calculates the probability density function (PDF) of the Poisson distribution.

Parameters

k	The number of events
lambda	The rate parameter (> 0)

Returns: The value of the PDF at k

Definition at line 160 of file pdfs.cpp.

                                                  {
     if (k < 0)
         return 0;
     else
         return std::exp(-lambda) * std::pow(lambda, k) /
                gpmp::core::Misc::factorial(k);
 }

References gpmp::core::Misc::factorial().

Referenced by main().

◆ rademacher()

double gpmp::stats::PDF::rademacher ( int k )

static

Calculates the probability density function (PDF) of the Rademacher distribution.

Parameters

k	The value (1 or -1)

Returns: The value of the PDF at k

Definition at line 169 of file pdfs.cpp.

                                      {
     if (k == -1)
         return 0.5;
     else if (k == 1)
         return 0.5;
     else
         return 0;
 }

Referenced by main().

◆ student_t()

double gpmp::stats::PDF::student_t	(	double	x,
		int	df
	)

static

Calculates the probability density function (PDF) of Student's t distribution.

Parameters

x	The value at which to evaluate the PDF
df	The degrees of freedom (> 0)

Returns: The value of the PDF at x

Definition at line 179 of file pdfs.cpp.

                                                {
     double numerator = std::tgamma((df + 1) / 2.0);
     double denominator = std::sqrt(df * M_PI) * std::tgamma(df / 2.0);
     return std::pow(1 + x * x / df, -(df + 1) / 2.0) * numerator / denominator;
 }

Referenced by main().

◆ uniform()

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

static

Calculates the probability density function (PDF) of the uniform distribution.

Parameters

x	The value at which to evaluate the PDF
a	The minimum value of the interval
b	The maximum value of the interval

Returns: The value of the PDF at x

Definition at line 186 of file pdfs.cpp.

                                                          {
     if (x >= a && x <= b)
         return 1 / (b - a);
     else
         return 0;
 }

Referenced by main().

◆ weibull()

double gpmp::stats::PDF::weibull	(	double	x,
		double	k,
		double	lambda
	)

static

Calculates the probability density function (PDF) of the Weibull distribution.

Parameters

x	The value at which to evaluate the PDF
k	The shape parameter (> 0)
lambda	The scale parameter (> 0)

Returns: The value of the PDF at x

Definition at line 194 of file pdfs.cpp.

                                                               {
     if (x < 0)
         return 0;
     else
         return (k / lambda) * std::pow(x / lambda, k - 1) *
                std::exp(-std::pow(x / lambda, k));
 }

Referenced by main().

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

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

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ bernoulli()

◆ beta()

◆ beta_function()

◆ binomial()

◆ binomial_coefficient()

◆ cauchy()

◆ chi_squared()

◆ exponential()

◆ f_dist()

◆ factorial()

◆ gamma()

◆ gaussian()

◆ inverse_gamma()

◆ inverse_gaussian()

◆ laplace()

◆ log_normal()

◆ logistic()

◆ poisson()

◆ rademacher()

◆ student_t()

◆ uniform()

◆ weibull()