Infinity::Engine::PoissonDistribution< IntType > Class Template Reference

Platform-independent Poisson distribution. More...

#include <PRNGDistribution.hpp>

Classes
struct	param_type
	Parameter set for the distribution. More...

Public Types
using	result_type = IntType
	The type of values produced by the distribution.

Public Member Functions
	PoissonDistribution ()
	Default constructor. Creates Poisson distribution with mean=1.0.
	PoissonDistribution (double mean)
	Constructs a Poisson distribution with specified mean.
	PoissonDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
double	mean () const
	Gets the mean (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 (0).
result_type	max () const
	Gets the theoretical maximum value (unbounded).
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 PoissonDistribution &lhs, const PoissonDistribution &rhs)
bool	operator!= (const PoissonDistribution &lhs, const PoissonDistribution &rhs)

Detailed Description

template<typename IntType = int>
class Infinity::Engine::PoissonDistribution< IntType >

Platform-independent Poisson distribution.

Produces integer counts of events occurring in a fixed interval when events happen independently at a constant average rate. Uses normal approximation for large means, Knuth's algorithm for small means.

The Poisson distribution is fundamental for modeling count data where events occur randomly over time or space: number of calls per hour, defects per item, particles detected per second, customers arriving per minute, or any process where events occur randomly at a constant average rate.

Template Parameters

IntType

Integer type for the result

Example usage:

PRNG rng(12345);
 
// Average 5 customers per hour
PoissonDistribution<int> customers(5.0);
int arrivals = customers(rng);
 
// Radioactive decay events (low rate)
PoissonDistribution<int> decay_events(2.3);
int detections = decay_events(rng);
 
// Web server requests per second
PoissonDistribution<int> requests(15.0);
int request_count = requests(rng);
 
// Procedural generation: enemy spawns per region
PoissonDistribution<int> spawns(3.5);
int enemy_count = spawns(rng);

Note

Returns non-negative integers.

Mean = Variance = mean parameter (equal mean and variance is characteristic).

Uses Knuth's method for mean < 10, normal approximation for mean >= 10.

For very large means (>100), normal approximation is highly accurate.

Member Typedef Documentation

result_type

template<typename IntType = int>

using Infinity::Engine::PoissonDistribution< IntType >::result_type = IntType

The type of values produced by the distribution.

Constructor & Destructor Documentation

PoissonDistribution() [1/3]

template<typename IntType = int>

Infinity::Engine::PoissonDistribution< IntType >::PoissonDistribution ( )

inline

Default constructor. Creates Poisson distribution with mean=1.0.

PoissonDistribution() [2/3]

template<typename IntType = int>

Infinity::Engine::PoissonDistribution< IntType >::PoissonDistribution ( double  mean )

inlineexplicit

Constructs a Poisson distribution with specified mean.

Parameters

mean	Mean number of events (rate parameter)

PoissonDistribution() [3/3]

template<typename IntType = int>

Infinity::Engine::PoissonDistribution< IntType >::PoissonDistribution ( const param_type &  param )

inlineexplicit

Constructs from a parameter set.

Parameters

param

The distribution parameters

Member Function Documentation

max()

template<typename IntType = int>

result_type Infinity::Engine::PoissonDistribution< IntType >::max ( ) const

inline

Gets the theoretical maximum value (unbounded).

mean()

template<typename IntType = int>

double Infinity::Engine::PoissonDistribution< IntType >::mean ( ) const

inline

Gets the mean (rate) parameter.

min()

template<typename IntType = int>

result_type Infinity::Engine::PoissonDistribution< IntType >::min ( ) const

inline

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

operator()() [1/2]

template<typename IntType = int>

template<typename Generator >

result_type Infinity::Engine::PoissonDistribution< IntType >::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 count of events

operator()() [2/2]

template<typename IntType = int>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

Uses two methods depending on the mean:

1. Normal approximation (mean >= 10): Uses Normal(mean, sqrt(mean)) with continuity correction. Fast and accurate for large means.

2. Knuth's method (mean < 10): Simulates the Poisson process by generating uniform random values and multiplying them until their product falls below e^(-mean). The count of multiplications gives the Poisson value.

   Algorithm: Generate U1, U2, ... ~ Uniform(0,1) Count k such that U1*U2*...*Uk > e^(-mean) Return k-1

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 count of events with mean param.mean()

param() [1/2]

template<typename IntType = int>

param_type Infinity::Engine::PoissonDistribution< IntType >::param ( ) const

inline

Gets the current parameter set.

param() [2/2]

template<typename IntType = int>

void Infinity::Engine::PoissonDistribution< IntType >::param ( const param_type &  param )

inline

Sets new parameters for the distribution.

Recreates the normal distribution for approximation if needed.

Parameters

param

The new distribution parameters

reset()

template<typename IntType = int>

void Infinity::Engine::PoissonDistribution< IntType >::reset ( )

inline

Resets the distribution state.

Resets the underlying normal distribution if it's being used for approximation.

Friends And Related Symbol Documentation

operator!=

template<typename IntType = int>

bool operator!= ( const PoissonDistribution< IntType > &  lhs, const PoissonDistribution< IntType > &  rhs  )

friend

operator==

template<typename IntType = int>

bool operator== ( const PoissonDistribution< IntType > &  lhs, const PoissonDistribution< IntType > &  rhs  )

friend