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

Platform-independent Fisher F-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
	FisherFDistribution ()
	Default constructor. Creates F(1, 1) distribution.
	FisherFDistribution (RealType m, RealType n=RealType(1))
	Constructs an F-distribution with specified degrees of freedom.
	FisherFDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
RealType	m () const
	Gets the numerator degrees of freedom.
RealType	n () const
	Gets the denominator 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 FisherFDistribution &lhs, const FisherFDistribution &rhs)
bool	operator!= (const FisherFDistribution &lhs, const FisherFDistribution &rhs)

Detailed Description

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

Platform-independent Fisher F-distribution.

Produces values according to the F-distribution with m and n degrees of freedom. The F-distribution arises naturally when comparing two chi-squared distributions, making it essential for analysis of variance (ANOVA) and comparing variances.

If X ~ ChiSquared(m) and Y ~ ChiSquared(n), then F = (X/m)/(Y/n) ~ F(m, n). This distribution is fundamental in statistical hypothesis testing, particularly for testing equality of variances and in regression analysis.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// F-distribution with 5 and 10 degrees of freedom
FisherFDistribution<float> f_dist(5.0f, 10.0f);
float value = f_dist(rng);
 
// ANOVA test statistic simulation
FisherFDistribution<double> anova_stat(3.0, 20.0);
for (int i = 0; i < 1000; ++i) {
    double f_value = anova_stat(rng);
}

Note

All values are strictly positive.

Mean = n/(n-2) for n > 2; undefined for n ≤ 2.

Variance = 2n²(m+n-2) / [m(n-2)²(n-4)] for n > 4.

As both m and n increase, the distribution becomes more symmetric.

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

FisherFDistribution() [1/3]

template<typename RealType = double>

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

inline

Default constructor. Creates F(1, 1) distribution.

FisherFDistribution() [2/3]

template<typename RealType = double>

Infinity::Engine::FisherFDistribution< RealType >::FisherFDistribution ( RealType  m, RealType  n = RealType(1)  )

inlineexplicit

Constructs an F-distribution with specified degrees of freedom.

Parameters

m	Numerator degrees of freedom
n	Denominator degrees of freedom

FisherFDistribution() [3/3]

template<typename RealType = double>

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

inlineexplicit

Constructs from a parameter set.

Parameters

param

The distribution parameters

Member Function Documentation

m()

template<typename RealType = double>

RealType Infinity::Engine::FisherFDistribution< RealType >::m ( ) const

inline

Gets the numerator degrees of freedom.

max()

template<typename RealType = double>

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

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

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

inline

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

n()

template<typename RealType = double>

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

inline

Gets the denominator degrees of freedom.

operator()() [1/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using stored parameters.

Generates two independent chi-squared variables and computes their ratio. Uses the relationship: F(m,n) = (ChiSquared(m)/m) / (ChiSquared(n)/n)

Template Parameters

Generator

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

Parameters

g	The random number generator

Returns

A positive random value from the F-distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

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 F(param.m(), param.n())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Sets new parameters for the distribution.

Recreates both underlying gamma distributions with the new parameters.

Parameters

param

The new distribution parameters

reset()

template<typename RealType = double>

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

inline

Resets the distribution state.

Resets both underlying gamma distributions.

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend