distributions.h File Reference

Probability distribution functions. More...

#include "../core/real_analysis.h"
#include "../algebra/vec.h"
#include "./statistics.h"
#include "../core/function.h"
#include "../core/special.h"

Go to the source code of this file.

Namespaces
	theoretica
	Main namespace of the library which contains all functions and objects.
	theoretica::stats
	Statistical functions.
	theoretica::distribution
	Probability distribution functions.

Functions
real	theoretica::stats::likelihood (const vec< real > &X, const vec< real > &theta, stat_function f)
	Compute the likelihood of a distribution <f> with the given parameters <theta> and measures <X> More...
real	theoretica::stats::log_likelihood (const vec< real > &X, const vec< real > &theta, stat_function f)
	Compute the log likelihood of a distribution <f> with the given parameters <theta> and measures <X> More...
real	theoretica::distribution::gaussian (real x, real X, real sigma)
	Gaussian distribution function.
real	theoretica::distribution::gaussian (real x, const vec< real > &theta)
	Wrapper for distribution::gaussian(real, real, real)
real	theoretica::distribution::bernoulli (unsigned int k, real p)
	Bernoulli distribution.
real	theoretica::distribution::bernoulli (real k, const vec< real > &theta)
	Wrapper for distribution::bernoulli(unsigned int, real)
real	theoretica::distribution::poisson (unsigned int k, real lambda)
	Poisson distribution.
real	theoretica::distribution::poisson (real k, const vec< real > &theta)
	Wrapper for distribution::poisson(unsigned int, real)
real	theoretica::distribution::binomial (unsigned int nu, unsigned int n, real p)
	Binomial distribution function.
real	theoretica::distribution::binomial (real nu, const vec< real > &theta)
	Wrapper for distribution::binomial(unsigned int, unsigned int, real)
real	theoretica::distribution::multinomial (std::vector< unsigned int > x, unsigned int n, unsigned int k, std::vector< real > p)
	Multinomial distribution.
real	theoretica::distribution::chi_squared (real x, unsigned int k)
	Chi-squared distribution.
real	theoretica::distribution::chi_squared (real x, const vec< real > &theta)
	Wrapper for distribution::chi_squared(real, unsigned int)
real	theoretica::distribution::gamma (real x, real alpha, real beta)
	Gamma distribution density function with parameters alpha (shape) and beta (rate)
real	theoretica::distribution::gamma (real x, const vec< real > &theta)
	Wrapper for distribution::gamma(real, real, real)
real	theoretica::distribution::beta (real x, real alpha, real beta)
	Beta distribution density function with parameters alpha (shape) and beta (shape)
real	theoretica::distribution::beta (real x, const vec< real > &theta)
	Wrapper for distribution::beta(real, real, real)
real	theoretica::distribution::student (real x, unsigned int nu)
	Student's t distribution.
real	theoretica::distribution::student (real x, const vec< real > &theta)
	Wrapper for distribution::student(real, unsigned int)
real	theoretica::distribution::log_normal (real x, real mu, real sigma)
	Log-normal distribution.
real	theoretica::distribution::log_normal (real x, const vec< real > &theta)
	Wrapper for distribution::log_normal(real, real, real)
real	theoretica::distribution::exponential (real x, real lambda)
	Exponential distribution.
real	theoretica::distribution::exponential (real x, const vec< real > &theta)
	Wrapper for distribution::exponential(real, real)
real	theoretica::distribution::rayleigh (real x, real sigma)
	Rayleigh distribution.
real	theoretica::distribution::rayleigh (real x, const vec< real > &theta)
	Wrapper for distribution::rayleigh(real, real)
real	theoretica::distribution::cauchy (real x, real mu, real alpha)
	Cauchy distribution.
real	theoretica::distribution::cauchy (real x, const vec< real > &theta)
	Wrapper for distribution::cauchy(real, real, real)
real	theoretica::distribution::breit_wigner (real x, real M, real Gamma)
	Breit Wigner distribution.
real	theoretica::distribution::breit_wigner (real x, const vec< real > &theta)
	Wrapper for distribution::breit_wigner(real, real, real)
real	theoretica::distribution::maxwell (real x, real a)
	Maxwell-Boltzmann distribution.
real	theoretica::distribution::maxwell (real x, const vec< real > &theta)
	Wrapper for distribution::maxwell(real, real)
real	theoretica::distribution::laplace (real x, real mu, real b)
	Laplace distribution.
real	theoretica::distribution::laplace (real x, const vec< real > &theta)
	Laplace distribution.
real	theoretica::distribution::pareto (real x, real x_m, real alpha)
	Pareto distribution.
real	theoretica::distribution::pareto (real x, const vec< real > &theta)
	Wrapper for distribution::pareto(real, real, real)
real	theoretica::distribution::erlang (real x, unsigned int k, real lambda)
	Erlang distribution.
real	theoretica::distribution::erlang (real x, const vec< real > &theta)
	Wrapper for distribution::erlang(real, unsigned int, real)

Detailed Description

Probability distribution functions.