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

Platform-independent Weibull 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
	WeibullDistribution ()
	Default constructor. Creates Weibull(1, 1) distribution.
	WeibullDistribution (RealType a, RealType b=RealType(1))
	Constructs a Weibull distribution with specified parameters.
	WeibullDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
RealType	a () const
	Gets the shape 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 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 WeibullDistribution &lhs, const WeibullDistribution &rhs)
bool	operator!= (const WeibullDistribution &lhs, const WeibullDistribution &rhs)

Detailed Description

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

Platform-independent Weibull distribution.

Produces positive values according to the Weibull distribution with shape parameter a and scale parameter b. Generalizes the exponential distribution and is widely used in reliability analysis and lifetime modeling.

The shape parameter determines the failure rate behavior:

• a < 1: Decreasing failure rate (infant mortality, early failures)
• a = 1: Constant failure rate (exponential distribution, random failures)
• a > 1: Increasing failure rate (wear-out failures, aging)

This makes the Weibull distribution extremely versatile for modeling component lifetimes across different failure modes.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// Shape=2, Scale=1 (Rayleigh distribution - wind speed modeling)
WeibullDistribution<float> wind_speed(2.0f, 1.0f);
float speed = wind_speed(rng);
 
// Component lifetime modeling (wear-out failures)
WeibullDistribution<float> lifetime(1.5f, 1000.0f);
float hours_to_failure = lifetime(rng);
 
// Infant mortality (decreasing failure rate)
WeibullDistribution<double> early_failure(0.8, 100.0);
double time_to_defect = early_failure(rng);

Note

All values are strictly positive.

When a = 2, b = sqrt(2), becomes Rayleigh distribution.

When a = 1, reduces to exponential distribution with rate 1/b.

Mean = b * Γ(1 + 1/a), where Γ is the gamma function.

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

WeibullDistribution() [1/3]

template<typename RealType = double>

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

inline

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

WeibullDistribution() [2/3]

template<typename RealType = double>

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

inlineexplicit

Constructs a Weibull distribution with specified parameters.

Parameters

a	Shape parameter
b	Scale parameter

WeibullDistribution() [3/3]

template<typename RealType = double>

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

inline

Gets the shape parameter.

b()

template<typename RealType = double>

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

inline

Gets the scale parameter.

max()

template<typename RealType = double>

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

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

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

inline

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

operator()() [1/2]

template<typename RealType = double>

template<typename Generator >

result_type Infinity::Engine::WeibullDistribution< 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 positive random value from the Weibull distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

Uses the transformation: If E ~ Exponential(1), then X = b * E^(1/a) ~ Weibull(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 positive random value from Weibull(param.a(), param.b())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Sets new parameters for the distribution.

reset()

template<typename RealType = double>

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

inline

Resets the distribution state.

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

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend