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

Platform-independent exponential 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
	ExponentialDistribution ()
	Default constructor. Creates Exponential(1) distribution.
	ExponentialDistribution (RealType lambda)
	Constructs an exponential distribution with specified rate.
	ExponentialDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
RealType	lambda () const
	Gets the rate 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 ExponentialDistribution &lhs, const ExponentialDistribution &rhs)
bool	operator!= (const ExponentialDistribution &lhs, const ExponentialDistribution &rhs)

Detailed Description

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

Platform-independent exponential distribution.

Produces positive values according to the exponential distribution with rate parameter lambda. Models time between events in a Poisson process, making it fundamental for modeling waiting times and lifetimes.

The exponential distribution is the continuous analog of the geometric distribution and is the only continuous distribution with the memoryless property: the probability of an event occurring in the next time interval is independent of how much time has already elapsed.

Template Parameters

RealType

Floating point type (float or double)

Example usage:

PRNG rng(12345);
 
// Average time between events = 1/lambda = 1/0.5 = 2.0 units
ExponentialDistribution<float> arrival_times(0.5f);
float wait_time = arrival_times(rng);
 
// Generate event intervals for a Poisson process
ExponentialDistribution<double> intervals(1.5);  // rate = 1.5 events per unit
double total_time = 0.0;
for (int i = 0; i < 10; ++i) {
    double interval = intervals(rng);
    total_time += interval;
}
 
// Model component failure times
ExponentialDistribution<float> failure_time(0.001f);  // low failure rate
float time_to_failure = failure_time(rng);

Note

All values are strictly positive.

Memoryless property: P(X > s+t | X > s) = P(X > t)

Mean = 1/lambda, Variance = 1/lambda²

Special case of Gamma(1, 1/lambda) distribution.

Member Typedef Documentation

result_type

template<typename RealType = double>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

ExponentialDistribution() [1/3]

template<typename RealType = double>

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

inline

Default constructor. Creates Exponential(1) distribution.

ExponentialDistribution() [2/3]

template<typename RealType = double>

Infinity::Engine::ExponentialDistribution< RealType >::ExponentialDistribution ( RealType  lambda )

inlineexplicit

Constructs an exponential distribution with specified rate.

Parameters

lambda

Rate parameter

ExponentialDistribution() [3/3]

template<typename RealType = double>

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

inlineexplicit

Constructs from a parameter set.

Parameters

param

The distribution parameters

Member Function Documentation

lambda()

template<typename RealType = double>

RealType Infinity::Engine::ExponentialDistribution< RealType >::lambda ( ) const

inline

Gets the rate parameter.

max()

template<typename RealType = double>

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

inline

Gets the theoretical maximum value (positive infinity).

min()

template<typename RealType = double>

result_type Infinity::Engine::ExponentialDistribution< 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::ExponentialDistribution< 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 exponential distribution

operator()() [2/2]

template<typename RealType = double>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

Uses the inverse CDF method: X = -ln(1-U) / lambda where U ~ Uniform(0, 1) and X ~ Exponential(lambda).

The implementation avoids U = 0 or 1 to prevent numerical issues.

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 Exponential(param.lambda())

param() [1/2]

template<typename RealType = double>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename RealType = double>

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

inline

Sets new parameters for the distribution.

reset()

template<typename RealType = double>

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

inline

Resets the distribution state.

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

Friends And Related Symbol Documentation

operator!=

template<typename RealType = double>

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

friend

operator==

template<typename RealType = double>

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

friend