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

Platform-independent Cauchy (Lorentz) 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
	CauchyDistribution ()
	Default constructor. Creates standard Cauchy distribution (a=0, b=1).
	CauchyDistribution (RealType a, RealType b=RealType(1))
	Constructs a Cauchy distribution with specified parameters.
	CauchyDistribution (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 CauchyDistribution &lhs, const CauchyDistribution &rhs)
bool	operator!= (const CauchyDistribution &lhs, const CauchyDistribution &rhs)

Detailed Description

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

Platform-independent Cauchy (Lorentz) distribution.

Produces values according to the Cauchy distribution, which has heavy tails and undefined mean and variance. Useful for modeling phenomena with extreme outliers or when you need occasional very large values.

The Cauchy distribution is notable for having no defined moments - the mean, variance, and higher moments do not exist mathematically. This makes it useful for modeling phenomena where extreme values occur much more frequently than in a normal distribution, such as resonance phenomena in physics or certain financial models.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// Standard Cauchy (location=0, scale=1)
CauchyDistribution<float> standard;
float value = standard(rng);
 
// Custom location and scale parameters
CauchyDistribution<float> custom(5.0f, 2.0f);
float shifted = custom(rng);
 
// Generate values with heavy tails for outlier modeling
CauchyDistribution<double> outliers(0.0, 1.0);
for (int i = 0; i < 100; ++i) {
    double val = outliers(rng);  // Expect occasional very large values
}

Note

Heavy-tailed: extreme values occur much more frequently than in normal distribution.

Mean and variance are undefined (do not exist mathematically).

The median and mode both equal the location parameter a.

Warning

Sample mean does not converge to any value as sample size increases.

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

CauchyDistribution() [1/3]

template<typename RealType = double>

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

inline

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

CauchyDistribution() [2/3]

template<typename RealType = double>

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

inlineexplicit

Constructs a Cauchy distribution with specified parameters.

Parameters

a	Location parameter
b	Scale parameter

CauchyDistribution() [3/3]

template<typename RealType = double>

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

inline

Gets the location parameter.

b()

template<typename RealType = double>

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

inline

Gets the scale parameter.

max()

template<typename RealType = double>

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

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

result_type Infinity::Engine::CauchyDistribution< 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::CauchyDistribution< 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 Cauchy distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

result_type Infinity::Engine::CauchyDistribution< 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 * tan(π(U - 0.5)) where U ~ Uniform(0, 1) and X ~ Cauchy(a, b).

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 Cauchy(param.a(), param.b())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Sets new parameters for the distribution.

reset()

template<typename RealType = double>

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

inline

Resets the distribution state.

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

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend