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

Platform-independent binomial 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
	BinomialDistribution ()
	Default constructor. Creates single trial distribution (t=1, p=0.5).
	BinomialDistribution (IntType t, double p=0.5)
	Constructs a binomial distribution with specified parameters.
	BinomialDistribution (const param_type &param)
	Constructs from a parameter set.
void	reset ()
	Resets the distribution state.
IntType	t () const
	Gets the number of trials.
double	p () const
	Gets the success probability.
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 maximum value that can be generated (t).
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 BinomialDistribution &lhs, const BinomialDistribution &rhs)
bool	operator!= (const BinomialDistribution &lhs, const BinomialDistribution &rhs)

Detailed Description

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

Platform-independent binomial distribution.

Produces integer counts of successes in t independent Bernoulli trials, each with success probability p. For large t*p and t*(1-p), uses normal approximation for efficiency; otherwise uses direct simulation.

The binomial distribution models the number of successes in a fixed number of independent yes/no trials, such as number of heads in coin flips, defective items in a batch, or hits in a series of attempts. It's one of the most fundamental discrete distributions in probability theory.

Template Parameters

IntType

Integer type for the result

Example usage:

PRNG rng(12345);
 
// Number of heads in 10 fair coin flips
BinomialDistribution<int> coins(10, 0.5);
int heads = coins(rng);  // Returns 0-10
 
// Quality control: defects in batch of 100 (2% defect rate)
BinomialDistribution<int> defects(100, 0.02);
int defective_count = defects(rng);
 
// Success rate in RPG combat system
BinomialDistribution<int> hits(5, 0.7);  // 5 attacks, 70% hit chance each
int successful_hits = hits(rng);
 
// Procedural generation: number of resources in region
BinomialDistribution<int> resources(20, 0.3);
int resource_count = resources(rng);

Note

Returns values in [0, t].

Mean = t*p, Variance = t*p*(1-p).

Uses normal approximation when t*p >= 5 and t*(1-p) >= 5 for efficiency.

For p very close to 0 or 1, consider using Poisson approximation separately.

Member Typedef Documentation

result_type

template<typename IntType = int>

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

The type of values produced by the distribution.

Constructor & Destructor Documentation

BinomialDistribution() [1/3]

template<typename IntType = int>

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

inline

Default constructor. Creates single trial distribution (t=1, p=0.5).

BinomialDistribution() [2/3]

template<typename IntType = int>

Infinity::Engine::BinomialDistribution< IntType >::BinomialDistribution ( IntType  t, double  p = 0.5  )

inlineexplicit

Constructs a binomial distribution with specified parameters.

Parameters

t	Number of trials
p	Success probability per trial

BinomialDistribution() [3/3]

template<typename IntType = int>

Infinity::Engine::BinomialDistribution< IntType >::BinomialDistribution ( 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::BinomialDistribution< IntType >::max ( ) const

inline

Gets the maximum value that can be generated (t).

min()

template<typename IntType = int>

result_type Infinity::Engine::BinomialDistribution< 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::BinomialDistribution< 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 successes in [0, t]

operator()() [2/2]

template<typename IntType = int>

template<typename Generator >

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

inline

Generates the next random value using provided parameters.

Uses two methods depending on parameters:

1. Normal approximation (when t*p >= 5 and t*(1-p) >= 5): Uses continuity correction and samples from Normal(t*p, sqrt(t*p*(1-p))), then rounds to nearest integer and clamps to valid range.
2. Direct simulation (small t or extreme p): Performs t independent Bernoulli trials and counts successes. Slower but exact for small numbers of trials.

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 successes in [0, param.t()]

p()

template<typename IntType = int>

double Infinity::Engine::BinomialDistribution< IntType >::p ( ) const

inline

Gets the success probability.

param() [1/2]

template<typename IntType = int>

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

inline

Gets the current parameter set.

param() [2/2]

template<typename IntType = int>

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

inline

Resets the distribution state.

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

t()

template<typename IntType = int>

IntType Infinity::Engine::BinomialDistribution< IntType >::t ( ) const

inline

Gets the number of trials.

Friends And Related Symbol Documentation

operator!=

template<typename IntType = int>

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

friend

operator==

template<typename IntType = int>

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

friend