The UnivariateDistribution class
Abstract class for all univariate probability distributions. More...

#include <univariate.hpp>

Inheritance diagram for randlib::UnivariateDistribution< T >:

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Collaboration diagram for randlib::UnivariateDistribution< T >:

Public Member Functions
virtual	~UnivariateDistribution ()

virtual Support	SupportType () const =0

bool	isLeftBounded () const

bool	isRightBounded () const

virtual long double	Mean () const =0

virtual long double	Variance () const =0

T	Quantile (double p) const

T	Quantile1m (double p) const

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

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

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

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

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

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

virtual T	Median () const

virtual T	Mode () const =0
	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.

virtual long double	Skewness () const

virtual long double	Kurtosis () const

virtual long double	ExcessKurtosis () const

virtual long double	SecondMoment () const

virtual long double	ThirdMoment () const

virtual long double	FourthMoment () const

virtual double	LikelihoodFunction (std::span< const T > sample) const =0

virtual double	LogLikelihoodFunction (std::span< const T > sample) const =0

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

virtual std::string	Name () const =0

virtual T	MinValue () const =0

virtual T	MaxValue () const =0

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)

Static Public Member Functions
static long double	GetSampleSum (std::span< const T > sample)

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

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

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

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

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

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

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

Protected Member Functions
	UnivariateDistribution ()

virtual std::complex< double >	CFImpl (double t) const

virtual long double	ExpectedValue (const std::function< double(T)> &funPtr, T minPoint, T maxPoint) const =0

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 T	variate (detail::EngineRef g) const =0
	Every concrete distribution implements this by calling its templated operator()

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
static bool	allElementsAreNotGreaterThan (T value, std::span< const T > sample)

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

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

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

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

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 T>
class randlib::UnivariateDistribution< T >

The UnivariateDistribution class
Abstract class for all univariate probability distributions.

Constructor & Destructor Documentation

◆ UnivariateDistribution()

template<typename T >

randlib::UnivariateDistribution< T >::UnivariateDistribution ( )

protected

◆ ~UnivariateDistribution()

template<typename T >

virtual randlib::UnivariateDistribution< T >::~UnivariateDistribution ( )

inlinevirtual

Member Function Documentation

◆ allElementsAreNonNegative()

template<typename T >

bool randlib::UnivariateDistribution< T >::allElementsAreNonNegative ( std::span< const T > sample )

staticprotected

Parameters

sample

Returns: true if all elements in sample are non-negative

◆ allElementsAreNotGreaterThan()

template<typename T >

bool randlib::UnivariateDistribution< T >::allElementsAreNotGreaterThan	(	T	value,
		std::span< const T >	sample
	)

staticprotected

Parameters

value
sample

Returns: true if all elements in sample are not greater than given value

◆ allElementsAreNotSmallerThan()

template<typename T >

bool randlib::UnivariateDistribution< T >::allElementsAreNotSmallerThan	(	T	value,
		std::span< const T >	sample
	)

staticprotected

Parameters

value
sample

Returns: true if all elements in sample are not smaller than given value

◆ allElementsArePositive()

template<typename T >

bool randlib::UnivariateDistribution< T >::allElementsArePositive ( std::span< const T > sample )

staticprotected

Parameters

sample

Returns: true if all elements in sample are positive

◆ CF()

template<typename T >

std::complex< double > randlib::UnivariateDistribution< T >::CF ( double t ) const

Parameters

t

Returns: CFImpl for t != 0 and 1 otherwise

◆ CFImpl()

template<typename T >

std::complex< double > randlib::UnivariateDistribution< T >::CFImpl ( double t ) const

protectedvirtual

Parameters

t

Returns: characteristic function implementation (inverse Fourier transform of pdf)

Reimplemented in randlib::WrappedExponentialRand< RealType >, randlib::BetaDistribution< RealType >, randlib::BetaDistribution< double >, randlib::GeneralGeometricStableDistribution< RealType >, randlib::NakagamiDistribution< RealType >, randlib::DiscreteDistribution< IntType >, randlib::DiscreteDistribution< int >, and randlib::DiscreteDistribution< long long int >.

◆ CharacteristicFunction()

template<typename T >

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

Parameters

t	input vector
y	output vector: y = CF(t)

◆ ExcessKurtosis()

template<typename T >

long double randlib::UnivariateDistribution< T >::ExcessKurtosis ( ) const

virtual

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

◆ ExpectedValue()

template<typename T >

virtual long double randlib::UnivariateDistribution< T >::ExpectedValue	(	const std::function< double(T)> &	funPtr,
		T	minPoint,
		T	maxPoint
	)		const

protectedpure virtual

Parameters

funPtr	pointer on function g(x) with finite support which expected value should be returned
minPoint	min{x \| g(x) ≠ 0}
maxPoint	max{x \| g(x) ≠ 0}

Returns: E[g(x)]

Implemented in randlib::DiscreteDistribution< IntType >, and randlib::ContinuousDistribution< RealType >.

◆ FourthMoment()

template<typename T >

long double randlib::UnivariateDistribution< T >::FourthMoment ( ) const

virtual

Returns: E[X^4]

Reimplemented in randlib::ExponentialRand< RealType >, randlib::NakagamiDistribution< RealType >, randlib::NormalRand< RealType >, randlib::PlanckRand< RealType >, randlib::StableCountRand< RealType >, randlib::ZetaRand< IntType >, and randlib::ZetaRand< long long int >.

◆ GetSampleLogMean()

template<typename T >

long double randlib::UnivariateDistribution< T >::GetSampleLogMean ( std::span< const T > sample )

static

Parameters

sample

Returns: arithmetic log-average

◆ GetSampleLogMeanAndVariance()

template<typename T >

LongDoublePair randlib::UnivariateDistribution< T >::GetSampleLogMeanAndVariance ( std::span< const T > sample )

static

Parameters

sample

Returns: sample log-mean and log-variance

Welford's stable method

◆ GetSampleLogVariance()

template<typename T >

long double randlib::UnivariateDistribution< T >::GetSampleLogVariance	(	std::span< const T >	sample,
		double	logMean
	)

static

Parameters

sample
logMean	known log-mean value

Returns: sample log-variance

◆ GetSampleMean()

template<typename T >

long double randlib::UnivariateDistribution< T >::GetSampleMean ( std::span< const T > sample )

static

Parameters

sample

Returns: arithmetic average

◆ GetSampleMeanAndVariance()

template<typename T >

LongDoublePair randlib::UnivariateDistribution< T >::GetSampleMeanAndVariance ( std::span< const T > sample )

static

Parameters

sample

Returns: sample mean and variance

Welford's stable method

◆ GetSampleStatistics()

template<typename T >

std::tuple< long double, long double, long double, long double > randlib::UnivariateDistribution< T >::GetSampleStatistics ( std::span< const T > sample )

static

Parameters

sample

Returns: sample mean, variance, skewness and excess kurtosis

Terriberry's extension for skewness and kurtosis

This looks like a hack and unfortunately it is. The reason of it is that the algorithm can become unstable for sufficiently large k. For now we restart the algorithm when k reaches some big number. In the future this can be parallelized for faster implementation.

M4

M3

M2 and M1

If something left - add the residue

M4

M3

M2 and M1

◆ GetSampleSum()

template<typename T >

long double randlib::UnivariateDistribution< T >::GetSampleSum ( std::span< const T > sample )

static

Parameters

sample

Returns: sum of all elements in a sample

◆ GetSampleVariance()

template<typename T >

long double randlib::UnivariateDistribution< T >::GetSampleVariance	(	std::span< const T >	sample,
		double	mean
	)

static

Parameters

sample
mean	known mean value

Returns: sample second central moment

◆ Hazard()

template<typename T >

virtual double randlib::UnivariateDistribution< T >::Hazard ( const T & x ) const

pure virtual

Parameters

x	input parameter

Returns: hazard function

Implemented in randlib::DiscreteDistribution< IntType >, and randlib::ContinuousDistribution< RealType >.

◆ HazardFunction()

template<typename T >

void randlib::UnivariateDistribution< T >::HazardFunction	(	std::span< const T >	x,
		std::span< double >	y
	)		const

Parameters

x	input vector
y	output vector: y = Hazard(x)

◆ isLeftBounded()

template<typename T >

bool randlib::UnivariateDistribution< T >::isLeftBounded ( ) const

Returns: true if distribution is bounded from the left

◆ isRightBounded()

template<typename T >

bool randlib::UnivariateDistribution< T >::isRightBounded ( ) const

Returns: true if distribution is bounded from the right

◆ Kurtosis()

template<typename T >

long double randlib::UnivariateDistribution< T >::Kurtosis ( ) const

virtual

Returns: unbiased kurtosis = μ_4 / σ ^ 4

◆ LikelihoodFunction()

template<typename T >

virtual double randlib::UnivariateDistribution< T >::LikelihoodFunction ( std::span< const T > sample ) const

pure virtual

Parameters

sample

Returns: likelihood function for given sample

Implemented in randlib::DiscreteDistribution< IntType >, randlib::UniformDiscreteRand< IntType >, randlib::UniformRand< RealType >, and randlib::ContinuousDistribution< RealType >.

◆ LogLikelihoodFunction()

template<typename T >

virtual double randlib::UnivariateDistribution< T >::LogLikelihoodFunction ( std::span< const T > sample ) const

pure virtual

Parameters

sample

Returns: logarithm of likelihood function for given sample

Implemented in randlib::DiscreteDistribution< IntType >, randlib::UniformDiscreteRand< IntType >, randlib::UniformRand< RealType >, and randlib::ContinuousDistribution< RealType >.

◆ Mean()

template<typename T >

virtual long double randlib::UnivariateDistribution< T >::Mean ( ) const

pure virtual

Returns: Mathematical expectation

◆ Median()

template<typename T >

T randlib::UnivariateDistribution< T >::Median ( ) const

virtual

Returns: such x that F(x) = 0.5

◆ Mode()

template<typename T >

virtual T randlib::UnivariateDistribution< T >::Mode ( ) const

pure virtual

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.

◆ Quantile()

template<typename T >

T randlib::UnivariateDistribution< T >::Quantile ( double p ) const

Parameters

p

Returns: quantileImpl(p) if p is in (0, 1)

◆ Quantile1m()

template<typename T >

T randlib::UnivariateDistribution< T >::Quantile1m ( double p ) const

Parameters

p

Returns: quantileImpl1m(p) if p is in (0, 1)

◆ QuantileFunction()

template<typename T >

void randlib::UnivariateDistribution< T >::QuantileFunction	(	std::span< const double >	p,
		std::span< T >	y
	)		const

Parameters

p
y	Fills vector y with Quantile(p)

◆ QuantileFunction1m()

template<typename T >

void randlib::UnivariateDistribution< T >::QuantileFunction1m	(	std::span< const double >	p,
		std::span< T >	y
	)		const

Parameters

p
y	Fills vector y with Quantile1m(p)

◆ SecondMoment()

template<typename T >

long double randlib::UnivariateDistribution< T >::SecondMoment ( ) const

virtual

Returns: E[X^2]

Reimplemented in randlib::PlanckRand< RealType >, and randlib::StableCountRand< RealType >.

◆ Skewness()

template<typename T >

long double randlib::UnivariateDistribution< T >::Skewness ( ) const

virtual

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

var is finite, so is mu

◆ SupportType()

template<typename T >

virtual Support randlib::UnivariateDistribution< T >::SupportType ( ) const

pure virtual

Returns: type of support

◆ ThirdMoment()

template<typename T >

long double randlib::UnivariateDistribution< T >::ThirdMoment ( ) const

virtual

Returns: E[X^3]

Reimplemented in randlib::ExponentialRand< RealType >, randlib::NormalRand< RealType >, randlib::PlanckRand< RealType >, randlib::StableCountRand< RealType >, randlib::ZetaRand< IntType >, and randlib::ZetaRand< long long int >.

◆ Variance()

template<typename T >

virtual long double randlib::UnivariateDistribution< T >::Variance ( ) const

pure virtual

Returns: Variance of random variable

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ UnivariateDistribution()

◆ ~UnivariateDistribution()

Member Function Documentation

◆ allElementsAreNonNegative()

◆ allElementsAreNotGreaterThan()

◆ allElementsAreNotSmallerThan()

◆ allElementsArePositive()

◆ CF()

◆ CFImpl()

◆ CharacteristicFunction()

◆ ExcessKurtosis()

◆ ExpectedValue()

◆ FourthMoment()

◆ GetSampleLogMean()

◆ GetSampleLogMeanAndVariance()

◆ GetSampleLogVariance()

◆ GetSampleMean()

◆ GetSampleMeanAndVariance()

◆ GetSampleStatistics()

◆ GetSampleSum()

◆ GetSampleVariance()

◆ Hazard()

◆ HazardFunction()

◆ isLeftBounded()

◆ isRightBounded()

◆ Kurtosis()

◆ LikelihoodFunction()

◆ LogLikelihoodFunction()

◆ Mean()

◆ Median()

◆ Mode()

◆ Quantile()

◆ Quantile1m()

◆ QuantileFunction()

◆ QuantileFunction1m()

◆ SecondMoment()

◆ Skewness()

◆ SupportType()

◆ ThirdMoment()

◆ Variance()