theoretica::distribution Namespace Reference

Probability distribution functions. More...

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

Detailed Description

Probability distribution functions.

Function Documentation

chi_squared() [1/2]

real theoretica::distribution::chi_squared ( real  x, unsigned int  k  )

inline

Chi-squared distribution.

Parameters

x	The point to evaluate the distribution at
k	The number of degrees of freedom

chi_squared() [2/2]

real theoretica::distribution::chi_squared ( real  x, unsigned int  k, real  half_gamma_k  )

inline

Chi-squared distribution.

Parameters

x	The point to evaluate the distribution at
k	The number of degrees of freedom
half_gamma_k	A precomputed value of special::half_gamma(k)

This function accepts a precomputed value of special::half_gamma(k) for repeated evaluation of the distribution. You can compute it once and reuse the same result for constant ndf.