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

Platform-independent extreme value (Gumbel) 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
	ExtremeValueDistribution ()
	Default constructor. Creates standard Gumbel distribution (a=0, b=1).
	ExtremeValueDistribution (RealType a, RealType b=RealType(1))
	Constructs an extreme value distribution with specified parameters.
	ExtremeValueDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
RealType	a () const
	Gets the location parameter.
RealType	b () const
	Gets the scale parameter.
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 ExtremeValueDistribution &lhs, const ExtremeValueDistribution &rhs)
bool	operator!= (const ExtremeValueDistribution &lhs, const ExtremeValueDistribution &rhs)

Detailed Description

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

Platform-independent extreme value (Gumbel) distribution.

Produces values according to the Type-I extreme value distribution (Gumbel distribution). Used to model the distribution of maximum (or minimum) values in a large sample, making it essential for modeling extreme events and rare occurrences.

The Gumbel distribution appears naturally as the limiting distribution of the maximum (or minimum) of a large number of independent, identically distributed random variables. Common applications include modeling floods, earthquake magnitudes, wind speeds, and other extreme weather events. It also appears in machine learning as the Gumbel-max trick for sampling from categorical distributions.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// Location=0, Scale=1 (standard Gumbel)
ExtremeValueDistribution<float> extreme;
float value = extreme(rng);
 
// Model annual maximum flood levels
ExtremeValueDistribution<float> flood_max(10.0f, 2.0f);
float max_level = flood_max(rng);
 
// Extreme wind speed modeling
ExtremeValueDistribution<double> wind_max(50.0, 5.0);
for (int i = 0; i < 100; ++i) {
    double max_speed = wind_max(rng);
}

Note

Distribution is asymmetric with a longer right tail.

Mean = a + γb where γ ≈ 0.5772 (Euler-Mascheroni constant).

Mode = a (the most likely value is the location parameter).

Variance = (π²/6) * b².

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

ExtremeValueDistribution() [1/3]

template<typename RealType = double>

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

inline

Default constructor. Creates standard Gumbel distribution (a=0, b=1).

ExtremeValueDistribution() [2/3]

template<typename RealType = double>

Infinity::Engine::ExtremeValueDistribution< RealType >::ExtremeValueDistribution ( RealType  a, RealType  b = RealType(1)  )

inlineexplicit

Constructs an extreme value distribution with specified parameters.

Parameters

a	Location parameter
b	Scale parameter

ExtremeValueDistribution() [3/3]

template<typename RealType = double>

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

inlineexplicit

Constructs from a parameter set.

Parameters

param

The distribution parameters

Member Function Documentation

a()

template<typename RealType = double>

RealType Infinity::Engine::ExtremeValueDistribution< RealType >::a ( ) const

inline

Gets the location parameter.

b()

template<typename RealType = double>

RealType Infinity::Engine::ExtremeValueDistribution< RealType >::b ( ) const

inline

Gets the scale parameter.

max()

template<typename RealType = double>

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

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

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

inline

Gets the theoretical minimum value (negative infinity).

operator()() [1/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using stored parameters.

Template Parameters

Generator

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

Parameters

g	The random number generator

Returns

A random value from the extreme value distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

Uses the inverse CDF method: X = a - b * ln(-ln(U)) where U ~ Uniform(0, 1) and X ~ Gumbel(a, b).

The double logarithm transformation creates the characteristic long right tail that makes this distribution suitable for modeling extreme maxima.

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 Gumbel(param.a(), param.b())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Sets new parameters for the distribution.

reset()

template<typename RealType = double>

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

inline

Resets the distribution state.

No-op for extreme value distribution as it maintains no internal state.

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend