Infinity::Engine::ChiSquaredDistribution< RealType > Class Template Reference

Platform-independent chi-squared distribution. More...

#include <PRNGDistribution.hpp>

Classes
struct	param_type
	Parameter set for the distribution. More...

Public Types
using	result_type = RealType
	The type of values produced by the distribution.

Public Member Functions
	ChiSquaredDistribution ()
	Default constructor. Creates ChiSquared(1) distribution.
	ChiSquaredDistribution (RealType n)
	Constructs a chi-squared distribution with specified degrees of freedom.
	ChiSquaredDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
RealType	n () const
	Gets the degrees of freedom.
param_type	param () const
	Gets the current parameter set.
void	param (const param_type &param)
	Sets new parameters for the distribution.
result_type	min () const
	Gets the minimum value that can be generated (approaches 0).
result_type	max () const
	Gets the theoretical maximum value (positive infinity).
template<typename Generator >
result_type	operator() (Generator &g)
	Generates the next random value using stored parameters.
template<typename Generator >
result_type	operator() (Generator &g, const param_type &param)
	Generates the next random value using provided parameters.

Friends
bool	operator== (const ChiSquaredDistribution &lhs, const ChiSquaredDistribution &rhs)
bool	operator!= (const ChiSquaredDistribution &lhs, const ChiSquaredDistribution &rhs)

Detailed Description

template<typename RealType = double>
class Infinity::Engine::ChiSquaredDistribution< RealType >

Platform-independent chi-squared distribution.

Produces values according to the chi-squared distribution with n degrees of freedom. The chi-squared distribution is a special case of the gamma distribution: ChiSquared(n) = Gamma(n/2, 2).

This distribution is fundamental in statistics, appearing in hypothesis testing, confidence intervals, and goodness-of-fit tests. It represents the distribution of the sum of squares of n independent standard normal random variables.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// Chi-squared with 5 degrees of freedom
ChiSquaredDistribution<float> chi2(5.0f);
float value = chi2(rng);
 
// Generate test statistics for goodness-of-fit
ChiSquaredDistribution<double> test_stat(10.0);
for (int i = 0; i < 1000; ++i) {
    double chi2_value = test_stat(rng);
}
 
// Model sum of squared standard normals
ChiSquaredDistribution<float> squared_sum(3.0f);
float sum_of_squares = squared_sum(rng);

Note

All values are strictly positive.

Mean = n, Variance = 2n

As n increases, the distribution approaches normal with mean n and variance 2n.

Related to normal: if Z ~ N(0,1), then Z² ~ ChiSquared(1)

Member Typedef Documentation

result_type

template<typename RealType = double>

using Infinity::Engine::ChiSquaredDistribution< RealType >::result_type = RealType

The type of values produced by the distribution.

Constructor & Destructor Documentation

ChiSquaredDistribution() [1/3]

template<typename RealType = double>

Infinity::Engine::ChiSquaredDistribution< RealType >::ChiSquaredDistribution ( )

inline

Default constructor. Creates ChiSquared(1) distribution.

ChiSquaredDistribution() [2/3]

template<typename RealType = double>

Infinity::Engine::ChiSquaredDistribution< RealType >::ChiSquaredDistribution ( RealType  n )

inlineexplicit

Constructs a chi-squared distribution with specified degrees of freedom.

Parameters

n	Degrees of freedom

ChiSquaredDistribution() [3/3]

template<typename RealType = double>

Infinity::Engine::ChiSquaredDistribution< RealType >::ChiSquaredDistribution ( const param_type &  param )

inlineexplicit

Constructs from a parameter set.

Parameters

param

The distribution parameters

Member Function Documentation

max()

template<typename RealType = double>

result_type Infinity::Engine::ChiSquaredDistribution< RealType >::max ( ) const

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

result_type Infinity::Engine::ChiSquaredDistribution< RealType >::min ( ) const

inline

Gets the minimum value that can be generated (approaches 0).

n()

template<typename RealType = double>

RealType Infinity::Engine::ChiSquaredDistribution< RealType >::n ( ) const

inline

Gets the degrees of freedom.

operator()() [1/2]

template<typename RealType = double>

template<typename Generator >

result_type Infinity::Engine::ChiSquaredDistribution< RealType >::operator() ( Generator &  g )

inline

Generates the next random value using stored parameters.

Uses the relationship ChiSquared(n) = Gamma(n/2, 2) by generating from the underlying gamma distribution.

Template Parameters

Generator

The random number generator type (e.g., PRNG)

Parameters

g	The random number generator

Returns

A positive random value from the chi-squared distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

result_type Infinity::Engine::ChiSquaredDistribution< RealType >::operator() ( Generator &  g, const param_type &  param  )

inline

Generates the next random value using provided parameters.

Creates a temporary gamma distribution and generates a chi-squared value.

Template Parameters

Generator

The random number generator type (e.g., PRNG)

Parameters

g	The random number generator
param	The distribution parameters to use for this generation

Returns

A positive random value from ChiSquared(param.n())

param() [1/2]

template<typename RealType = double>

param_type Infinity::Engine::ChiSquaredDistribution< RealType >::param ( ) const

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

void Infinity::Engine::ChiSquaredDistribution< RealType >::param ( const param_type &  param )

inline

Sets new parameters for the distribution.

Recreates the underlying gamma distribution with the new degrees of freedom.

Parameters

param

The new distribution parameters

reset()

template<typename RealType = double>

void Infinity::Engine::ChiSquaredDistribution< RealType >::reset ( )

inline

Resets the distribution state.

Resets the underlying gamma distribution.

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

bool operator!= ( const ChiSquaredDistribution< RealType > &  lhs, const ChiSquaredDistribution< RealType > &  rhs  )

friend

operator==

template<typename RealType = double>

bool operator== ( const ChiSquaredDistribution< RealType > &  lhs, const ChiSquaredDistribution< RealType > &  rhs  )

friend