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

Platform-independent Student's t-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
	StudentTDistribution ()
	Default constructor. Creates t(1) distribution (Cauchy).
	StudentTDistribution (RealType n)
	Constructs a t-distribution with specified degrees of freedom.
	StudentTDistribution (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 theoretical minimum value (negative infinity).
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 StudentTDistribution &lhs, const StudentTDistribution &rhs)
bool	operator!= (const StudentTDistribution &lhs, const StudentTDistribution &rhs)

Detailed Description

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

Platform-independent Student's t-distribution.

Produces values according to Student's t-distribution with n degrees of freedom. Similar to the normal distribution but with heavier tails, approaching normal as n increases. Essential for statistical inference with small sample sizes.

The t-distribution arises when estimating the mean of a normally distributed population with unknown variance from small samples. It's widely used in confidence intervals and hypothesis tests when the sample size is small.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// t-distribution with 10 degrees of freedom
StudentTDistribution<float> t_dist(10.0f);
float value = t_dist(rng);
 
// Small sample confidence interval simulation
StudentTDistribution<double> small_sample(5.0);
for (int i = 0; i < 1000; ++i) {
    double t_value = small_sample(rng);
}
 
// Compare to normal for large n
StudentTDistribution<float> nearly_normal(100.0f);

Note

Symmetric around zero with heavier tails than normal distribution.

As n approaches infinity, converges to standard normal N(0,1).

Mean = 0 for n > 1; undefined for n ≤ 1.

Variance = n/(n-2) for n > 2; infinite for 1 < n ≤ 2; undefined for n ≤ 1.

For n = 1, reduces to Cauchy distribution.

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

StudentTDistribution() [1/3]

template<typename RealType = double>

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

inline

Default constructor. Creates t(1) distribution (Cauchy).

StudentTDistribution() [2/3]

template<typename RealType = double>

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

inlineexplicit

Constructs a t-distribution with specified degrees of freedom.

Parameters

n	Degrees of freedom

StudentTDistribution() [3/3]

template<typename RealType = double>

Infinity::Engine::StudentTDistribution< RealType >::StudentTDistribution ( 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::StudentTDistribution< RealType >::max ( ) const

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

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

inline

Gets the theoretical minimum value (negative infinity).

n()

template<typename RealType = double>

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

inline

Gets the degrees of freedom.

operator()() [1/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using stored parameters.

Uses the relationship: If Z ~ N(0,1) and V ~ ChiSquared(n), then T = Z / sqrt(V/n) ~ t(n)

Template Parameters

Generator

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

Parameters

g	The random number generator

Returns

A random value from the t-distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

result_type Infinity::Engine::StudentTDistribution< 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 random value from t(param.n())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Resets the distribution state.

Resets both the normal and gamma distributions.

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend