The PoissonRand class
Poisson distribution. More...

#include <poisson.hpp>

Inheritance diagram for randlib::PoissonRand< IntType >:

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Collaboration diagram for randlib::PoissonRand< IntType >:

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Public Member Functions
	PoissonRand (double rate=1.0)

std::string	Name () const override

Support	SupportType () const override

IntType	MinValue () const override

IntType	MaxValue () const override

void	SetRate (double rate)

double	GetRate () const noexcept

double	SufficientStatistic (IntType x) const override

double	SourceParameters () const override

double	SourceToNatural (double sourceParameters) const override

double	NaturalParameters () const override

double	LogNormalizer (double theta) const override

double	LogNormalizerGradient (double theta) const override

double	CarrierMeasure (IntType x) const override

double	CrossEntropyAdjusted (double parameters) const override

double	EntropyAdjusted () const override

double	logP (const IntType &k) const override

double	F (const IntType &k) const override

double	S (const IntType &k) const override

template<std::uniform_random_bit_generator G>
IntType	operator() (G &g) const

long double	Mean () const override

long double	Variance () const override

IntType	Median () const override

IntType	Mode () const override
	Mode is the value, which has the largest probability to happen, or, in the case of continuous distribution, has the largest value of density function.

long double	Skewness () const override

long double	ExcessKurtosis () const override

void	Fit (std::span< const IntType > sample)
	fit rate λ via maximum-likelihood method

void	Fit (std::span< const IntType > sample, DoublePair &confidenceInterval, double significanceLevel)
	Fit.

GammaRand	FitBayes (std::span< const IntType > sample, const GammaDistribution<> &priorDistribution, bool MAP=false)
	fit rate λ via Bayes estimation

Public Member Functions inherited from randlib::DiscreteDistribution< IntType >
virtual	~DiscreteDistribution ()

virtual double	P (const IntType &k) const

void	ProbabilityMassFunction (std::span< const IntType > x, std::span< double > y) const
	fill vector y with P(x)

void	LogProbabilityMassFunction (std::span< const IntType > x, std::span< double > y) const
	fill vector y with logP(x)

double	Hazard (const IntType &x) const override

double	LikelihoodFunction (std::span< const IntType > sample) const override

double	LogLikelihoodFunction (std::span< const IntType > sample) const override

bool	PearsonChiSquaredTest (std::span< const IntType > orderStatistic, double alpha, int lowerBoundary, int upperBoundary, size_t numberOfEstimatedParameters=0) const

bool	PearsonChiSquaredTest (std::span< const IntType > orderStatistic, double alpha, size_t numberOfEstimatedParameters=0) const

Public Member Functions inherited from randlib::UnivariateDistribution< IntType >
virtual	~UnivariateDistribution ()

bool	isLeftBounded () const

bool	isRightBounded () const

IntType	Quantile (double p) const

IntType	Quantile1m (double p) const

void	QuantileFunction (std::span< const double > p, std::span< IntType > y) const

void	QuantileFunction1m (std::span< const double > p, std::span< IntType > y) const

std::complex< double >	CF (double t) const

void	CharacteristicFunction (std::span< const double > t, std::span< std::complex< double > > y) const

void	HazardFunction (std::span< const IntType > x, std::span< double > y) const

virtual long double	Kurtosis () const

virtual long double	SecondMoment () const

virtual long double	ThirdMoment () const

virtual long double	FourthMoment () const

Public Member Functions inherited from randlib::ProbabilityDistribution< T >
virtual	~ProbabilityDistribution ()=default

virtual double	F (const T &x) const =0

void	CumulativeDistributionFunction (std::span< const T > x, std::span< double > y) const

virtual double	S (const T &x) const

void	SurvivalFunction (std::span< const T > x, std::span< double > y) const

template<std::uniform_random_bit_generator G>
T	operator() (G &g) const
	Draws a variate with the given engine through the virtual interface.

T	Variate () const
	Uses the engine of this object, so it is not thread-safe for one object; use operator() with one engine per thread instead.

void	Sample (std::span< T > outputData) const
	Fills the output with variates drawn with the engine of this object.

template<std::uniform_random_bit_generator G>
void	Sample (G &g, std::span< T > outputData) const
	Fills the output with variates drawn with the given engine.

void	Reseed (std::uint64_t seed)

Public Member Functions inherited from randlib::ExponentialFamily< IntType, double >
	ExponentialFamily ()

virtual	~ExponentialFamily ()

double	ProbabilityMeasure (IntType x) const

double	LogProbabilityMeasure (IntType x) const

double	KullbackLeiblerDivergence (double parameters) const

virtual double	CrossEntropyAdjusted (double parameters) const

Static Public Member Functions
template<std::uniform_random_bit_generator G>
static IntType	Variate (double rate, G &g)

Static Public Member Functions inherited from randlib::UnivariateDistribution< IntType >
static long double	GetSampleSum (std::span< const IntType > sample)

static long double	GetSampleMean (std::span< const IntType > sample)

static long double	GetSampleLogMean (std::span< const IntType > sample)

static long double	GetSampleVariance (std::span< const IntType > sample, double mean)

static long double	GetSampleLogVariance (std::span< const IntType > sample, double logMean)

static LongDoublePair	GetSampleMeanAndVariance (std::span< const IntType > sample)

static LongDoublePair	GetSampleLogMeanAndVariance (std::span< const IntType > sample)

static std::tuple< long double, long double, long double, long double >	GetSampleStatistics (std::span< const IntType > sample)

Additional Inherited Members
Public Types inherited from randlib::ProbabilityDistribution< T >
using	value_type = T

Protected Member Functions inherited from randlib::DiscreteDistribution< IntType >
	DiscreteDistribution ()

IntType	quantileImpl (double p, IntType initValue) const override

IntType	quantileImpl (double p) const override

IntType	quantileImpl1m (double p, IntType initValue) const override

IntType	quantileImpl1m (double p) const override

long double	ExpectedValue (const std::function< double(IntType)> &funPtr, IntType minPoint, IntType maxPoint) const override

Protected Member Functions inherited from randlib::UnivariateDistribution< IntType >
	UnivariateDistribution ()

Protected Member Functions inherited from randlib::ProbabilityDistribution< T >
std::string	toStringWithPrecision (const double a_value, const int n=6) const

	ProbabilityDistribution ()=default

DefaultEngine &	engine () const

virtual void	sample (detail::EngineRef g, std::span< T > outputData) const
	Fills the output with variate(g); distributions with a faster bulk algorithm override it.

fit_error	fitError (FitErrorCode code, const std::string &explanation) const

Static Protected Member Functions inherited from randlib::UnivariateDistribution< IntType >
static bool	allElementsAreNotGreaterThan (IntType value, std::span< const IntType > sample)

static bool	allElementsAreNotSmallerThan (IntType value, std::span< const IntType > sample)

static bool	allElementsAreNonNegative (std::span< const IntType > sample)

static bool	allElementsArePositive (std::span< const IntType > sample)

Static Protected Attributes inherited from randlib::ProbabilityDistribution< T >
static constexpr size_t	MAX_ITER_REJECTION = detail::MAX_ITER_REJECTION
	MAX_ITER_REJECTION upper boundary for maximum amount of iterations in rejection methods one thousand should be enough to be sure there is a bug (or rejection method is too slow to be used)

static constexpr char	POSITIVITY_VIOLATION [] = "All elements should be positive"

static constexpr char	NON_NEGATIVITY_VIOLATION [] = "All elements should be non-negative"

static constexpr char	UPPER_LIMIT_VIOLATION [] = "No element should be greater than "

static constexpr char	LOWER_LIMIT_VIOLATION [] = "No element should be smaller than "

Detailed Description

template<typename IntType>
class randlib::PoissonRand< IntType >

The PoissonRand class
Poisson distribution.

P(X = k) = λ^k * exp(-λ) / k!

Notation: X ~ Po(λ)

Constructor & Destructor Documentation

◆ PoissonRand()

template<typename IntType >

randlib::PoissonRand< IntType >::PoissonRand ( double rate = 1.0 )

explicit

Member Function Documentation

◆ CarrierMeasure()

template<typename IntType >

double randlib::PoissonRand< IntType >::CarrierMeasure ( IntType x ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ CrossEntropyAdjusted()

template<typename IntType >

double randlib::PoissonRand< IntType >::CrossEntropyAdjusted ( double parameters ) const

override

◆ EntropyAdjusted()

template<typename IntType >

double randlib::PoissonRand< IntType >::EntropyAdjusted ( ) const

overridevirtual

Reimplemented from randlib::ExponentialFamily< IntType, double >.

◆ ExcessKurtosis()

template<typename IntType >

long double randlib::PoissonRand< IntType >::ExcessKurtosis ( ) const

overridevirtual

Returns: E[((X - μ) / σ) ^ 4] - 3 (fourth moment around the mean divided by the square of the variance of the probability distribution minus 3)

var is finite, so is mu

Reimplemented from randlib::UnivariateDistribution< IntType >.

◆ F()

template<typename IntType >

double randlib::PoissonRand< IntType >::F ( const IntType & k ) const

override

◆ Fit() [1/2]

template<typename IntType >

void randlib::PoissonRand< IntType >::Fit ( std::span< const IntType > sample )

fit rate λ via maximum-likelihood method

Parameters

sample

◆ Fit() [2/2]

template<typename IntType >

void randlib::PoissonRand< IntType >::Fit	(	std::span< const IntType >	sample,
		DoublePair &	confidenceInterval,
		double	significanceLevel
	)

Fit.

Parameters

sample
confidenceInterval
significanceLevel

◆ FitBayes()

template<typename IntType >

GammaRand randlib::PoissonRand< IntType >::FitBayes	(	std::span< const IntType >	sample,
		const GammaDistribution<> &	priorDistribution,
		bool	MAP = `false`
	)

fit rate λ via Bayes estimation

Parameters

sample
priorDistribution
MAP	if true, use MAP estimator

Returns: posterior Gamma distribution

◆ GetRate()

template<typename IntType >

double randlib::PoissonRand< IntType >::GetRate ( ) const

inlinenoexcept

◆ LogNormalizer()

template<typename IntType >

double randlib::PoissonRand< IntType >::LogNormalizer ( double theta ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ LogNormalizerGradient()

template<typename IntType >

double randlib::PoissonRand< IntType >::LogNormalizerGradient ( double theta ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ logP()

template<typename IntType >

double randlib::PoissonRand< IntType >::logP ( const IntType & x ) const

overridevirtual

Parameters

x

Returns: logarithm of probability to get x

saddle-point form; k log λ - λ - log(k!) cancels catastrophically for large k

Implements randlib::DiscreteDistribution< IntType >.

◆ MaxValue()

template<typename IntType >

IntType randlib::PoissonRand< IntType >::MaxValue ( ) const

inlineoverridevirtual

Returns: maximum possible value that can be achieved by random variable

Implements randlib::ProbabilityDistribution< T >.

◆ Mean()

template<typename IntType >

long double randlib::PoissonRand< IntType >::Mean ( ) const

overridevirtual

Returns: Mathematical expectation

Implements randlib::UnivariateDistribution< IntType >.

◆ Median()

template<typename IntType >

IntType randlib::PoissonRand< IntType >::Median ( ) const

overridevirtual

Returns: such x that F(x) = 0.5

this value is approximate

Reimplemented from randlib::UnivariateDistribution< IntType >.

◆ MinValue()

template<typename IntType >

IntType randlib::PoissonRand< IntType >::MinValue ( ) const

inlineoverridevirtual

Returns: minimum possible value that can be achieved by random variable

Implements randlib::ProbabilityDistribution< T >.

◆ Mode()

template<typename IntType >

IntType randlib::PoissonRand< IntType >::Mode ( ) const

overridevirtual

Mode is the value, which has the largest probability to happen, or, in the case of continuous distribution, has the largest value of density function.

Returns: mode. In case, when it's not unique, return any of them.

Works only for unimodal distributions

Reimplemented from randlib::DiscreteDistribution< IntType >.

◆ Name()

template<typename IntType >

std::string randlib::PoissonRand< IntType >::Name ( ) const

overridevirtual

Returns: title of distribution, for instance "Normal(0, 1)"

Implements randlib::ProbabilityDistribution< T >.

◆ NaturalParameters()

template<typename IntType >

double randlib::PoissonRand< IntType >::NaturalParameters ( ) const

overridevirtual

Reimplemented from randlib::ExponentialFamily< IntType, double >.

◆ operator()()

template<typename IntType >

template<std::uniform_random_bit_generator G>

IntType randlib::PoissonRand< IntType >::operator() ( G & g ) const

◆ S()

template<typename IntType >

double randlib::PoissonRand< IntType >::S ( const IntType & k ) const

override

◆ SetRate()

template<typename IntType >

void randlib::PoissonRand< IntType >::SetRate ( double rate )

◆ Skewness()

template<typename IntType >

long double randlib::PoissonRand< IntType >::Skewness ( ) const

overridevirtual

Returns: E[((X - μ) / σ) ^ 3] where μ is central moment and σ is standard deviation

var is finite, so is mu

Reimplemented from randlib::UnivariateDistribution< IntType >.

◆ SourceParameters()

template<typename IntType >

double randlib::PoissonRand< IntType >::SourceParameters ( ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ SourceToNatural()

template<typename IntType >

double randlib::PoissonRand< IntType >::SourceToNatural ( double sourceParameters ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ SufficientStatistic()

template<typename IntType >

double randlib::PoissonRand< IntType >::SufficientStatistic ( IntType x ) const

overridevirtual

Implements randlib::ExponentialFamily< IntType, double >.

◆ SupportType()

template<typename IntType >

Support randlib::PoissonRand< IntType >::SupportType ( ) const

inlineoverridevirtual

Returns: type of support

Implements randlib::UnivariateDistribution< IntType >.

◆ Variance()

template<typename IntType >

long double randlib::PoissonRand< IntType >::Variance ( ) const

overridevirtual

Returns: Variance of random variable

Implements randlib::UnivariateDistribution< IntType >.

◆ Variate()

template<typename IntType >

template<std::uniform_random_bit_generator G>

IntType randlib::PoissonRand< IntType >::Variate	(	double	rate,
		G &	g
	)

static

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PoissonRand()

Member Function Documentation

◆ CarrierMeasure()

◆ CrossEntropyAdjusted()

◆ EntropyAdjusted()

◆ ExcessKurtosis()

◆ F()

◆ Fit() [1/2]

◆ Fit() [2/2]

◆ FitBayes()

◆ GetRate()

◆ LogNormalizer()

◆ LogNormalizerGradient()

◆ logP()

◆ MaxValue()

◆ Mean()

◆ Median()

◆ MinValue()

◆ Mode()

◆ Name()

◆ NaturalParameters()

◆ operator()()

◆ S()

◆ SetRate()

◆ Skewness()

◆ SourceParameters()

◆ SourceToNatural()

◆ SufficientStatistic()

◆ SupportType()

◆ Variance()

◆ Variate()