The GeneralGeometricStableDistribution class Abstract class for general interface of Asymmetric Laplace and Geometric-Stable distributions. More...

#include <geometric_stable.hpp>

Inheritance diagram for randlib::GeneralGeometricStableDistribution< RealType >:

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Collaboration diagram for randlib::GeneralGeometricStableDistribution< RealType >:

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Public Member Functions
virtual	~GeneralGeometricStableDistribution ()

double	GetExponent () const noexcept

double	GetSkewness () const noexcept

double	GetScale () const noexcept

double	GetLogScale () const noexcept

Support	SupportType () const override

RealType	MinValue () const override

RealType	MaxValue () const override

double	f (const RealType &x) const override

double	logf (const RealType &x) const override

double	F (const RealType &x) const override

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

long double	Mean () const override

long double	Variance () const override

RealType	Median () const override

RealType	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

Public Member Functions inherited from randlib::ContinuousDistribution< RealType >
virtual	~ContinuousDistribution ()

void	ProbabilityDensityFunction (std::span< const RealType > x, std::span< double > y) const
	fill vector y with f(x)

void	LogProbabilityDensityFunction (std::span< const RealType > x, std::span< double > y) const
	fill vector y with logf(x)

double	Hazard (const RealType &x) const override

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

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

bool	KolmogorovSmirnovTest (std::span< const RealType > orderStatistic, double alpha) const

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

bool	isLeftBounded () const

bool	isRightBounded () const

RealType	Quantile (double p) const

RealType	Quantile1m (double p) const

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

void	QuantileFunction1m (std::span< const double > p, std::span< RealType > 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 RealType > 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 std::string	Name () 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)

Protected Types
enum	DISTRIBUTION_TYPE { LAPLACE , ASYMMETRIC_LAPLACE , CAUCHY , LEVY , UNITY_EXPONENT , ONEHALF_EXPONENT , GENERAL }

Protected Member Functions
	GeneralGeometricStableDistribution (double exponent, double skewness, double scale=1.0, double location=0.0, double shift=0.0)
	log(κ)

void	SetParameters (double exponent, double skewness, double scale=1.0, double location=0.0, double shift=0.)

void	SetLocation (double location)

void	SetShift (double shift)

void	SetScale (double scale)

void	SetAsymmetry (double asymmetry)

double	pdfLaplace (double x) const

double	logpdfLaplace (double x) const

double	cdfLaplace (double x) const

double	cdfLaplaceCompl (double x) const

RealType	quantileLaplace (double p) const

RealType	quantileLaplace1m (double p) const

RealType	searchTailQuantile (double p, bool upperTail) const
	Quantile search that starts far tails from their power-law asymptote.

RealType	quantileImpl (double p) const override

RealType	quantileImpl1m (double p) const override

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

Protected Member Functions inherited from randlib::ContinuousDistribution< RealType >
	ContinuousDistribution ()

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

RealType	quantileImpl (double p, RealType initValue) const override

RealType	quantileImpl1m (double p, RealType initValue) const override

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

RealType	searchQuantile (double p, bool upperTail, RealType guess, double relativeStep=1e-3) const
	Deterministic root search for the quantile: brackets the root, starting from the guess when it is finite, then refines it with the Illinois variant of regula falsi (on a logarithmic scale for small p), falling back to bisection whenever the bracket does not halve.

Protected Member Functions inherited from randlib::UnivariateDistribution< RealType >
	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

Protected Attributes
double	alpha = 2
	characteristic exponent α

double	alphaInv = 0.5

double	beta = 0
	1/α

double	mu = 0
	location μ

double	m = 0
	shift m

double	gamma = randlib::consts::sqrt2
	scale γ

double	logGamma = 0.5 * randlib::consts::ln2
	log(γ)

double	kappa = 1
	parameters for α = 2

double	kappaInv = 1
	1 / κ

double	kappaSq = 1
	κ^2

double	log1pKappaSq = randlib::consts::ln2
	log(1 + κ^2)

double	logKappa = 0

DISTRIBUTION_TYPE	distributionType = LAPLACE
	type of distribution (Laplace by default)

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

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

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

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

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

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

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

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

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

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

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

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

static bool	allElementsArePositive (std::span< const RealType > 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 RealType>
class randlib::GeneralGeometricStableDistribution< RealType >

The GeneralGeometricStableDistribution class Abstract class for general interface of Asymmetric Laplace and Geometric-Stable distributions.

Member Enumeration Documentation

◆ DISTRIBUTION_TYPE

template<typename RealType >

enum randlib::GeneralGeometricStableDistribution::DISTRIBUTION_TYPE

protected

Enumerator
LAPLACE	α = 2, μ = 0
ASYMMETRIC_LAPLACE	α = 2, μ ≠ 0
CAUCHY	α = 1, β = 0
LEVY	α = 0.5, \|β\| = 1
UNITY_EXPONENT	α = 1, β ≠ 0
ONEHALF_EXPONENT	α = 0.5, \|β\| ≠ 1
GENERAL	the rest

Constructor & Destructor Documentation

◆ GeneralGeometricStableDistribution()

template<typename RealType >

randlib::GeneralGeometricStableDistribution< RealType >::GeneralGeometricStableDistribution	(	double	exponent,
		double	skewness,
		double	scale = `1.0`,
		double	location = `0.0`,
		double	shift = `0.0`
	)

protected

log(κ)

◆ ~GeneralGeometricStableDistribution()

template<typename RealType >

virtual randlib::GeneralGeometricStableDistribution< RealType >::~GeneralGeometricStableDistribution ( )

inlinevirtual

Member Function Documentation

◆ cdfLaplace()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::cdfLaplace ( double x ) const

protected

◆ cdfLaplaceCompl()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::cdfLaplaceCompl ( double x ) const

protected

◆ CFImpl()

template<typename RealType >

std::complex< double > randlib::GeneralGeometricStableDistribution< RealType >::CFImpl ( double t ) const

overrideprotectedvirtual

Parameters

t

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

Reimplemented from randlib::UnivariateDistribution< RealType >.

◆ ExcessKurtosis()

template<typename RealType >

long double randlib::GeneralGeometricStableDistribution< RealType >::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< RealType >.

◆ f()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::f ( const RealType & x ) const

overridevirtual

Parameters

x

Returns: probability density function

Cut zeros for semi-infinite distribution

Verify if any of analytical expressions is applicable

For α = 1, small w would need the stable law far in its tails, where it is slow (#1); integrate in z = exp(-w) instead

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ F()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::F ( const RealType & x ) const

override

For α = 1, integrate in t = z / (1 - z) instead (see f)

◆ GetExponent()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::GetExponent ( ) const

inlinenoexcept

◆ GetLogScale()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::GetLogScale ( ) const

inlinenoexcept

◆ GetScale()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::GetScale ( ) const

inlinenoexcept

◆ GetSkewness()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::GetSkewness ( ) const

inlinenoexcept

◆ logf()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::logf ( const RealType & x ) const

overridevirtual

Parameters

x

Returns: logarithm of probability density function

Implements randlib::ContinuousDistribution< RealType >.

◆ logpdfLaplace()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::logpdfLaplace ( double x ) const

protected

◆ MaxValue()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::MaxValue ( ) const

overridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mean()

template<typename RealType >

long double randlib::GeneralGeometricStableDistribution< RealType >::Mean ( ) const

overridevirtual

Returns: Mathematical expectation

Implements randlib::UnivariateDistribution< RealType >.

◆ Median()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::Median ( ) const

overridevirtual

Returns: such x that F(x) = 0.5

Reimplemented from randlib::UnivariateDistribution< RealType >.

◆ MinValue()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::MinValue ( ) const

overridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mode()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::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.

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ operator()()

template<typename RealType >

template<std::uniform_random_bit_generator G>

RealType randlib::GeneralGeometricStableDistribution< RealType >::operator() ( G & g ) const

◆ pdfLaplace()

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::pdfLaplace ( double x ) const

protected

◆ quantileImpl()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::quantileImpl ( double p ) const

overrideprotectedvirtual

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ quantileImpl1m()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::quantileImpl1m ( double p ) const

overrideprotectedvirtual

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ quantileLaplace()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::quantileLaplace ( double p ) const

protected

Parameters

p	input parameter in the interval (0, 1)

Returns: quantile for (Asymmetric) Laplace distribution

◆ quantileLaplace1m()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::quantileLaplace1m ( double p ) const

protected

Parameters

p	input parameter in the interval (0, 1)

Returns: quantile of 1-p for (Asymmetric) Laplace distribution

◆ searchTailQuantile()

template<typename RealType >

RealType randlib::GeneralGeometricStableDistribution< RealType >::searchTailQuantile	(	double	p,
		bool	upperTail
	)		const

protected

Quantile search that starts far tails from their power-law asymptote.

◆ SetAsymmetry()

template<typename RealType >

void randlib::GeneralGeometricStableDistribution< RealType >::SetAsymmetry ( double asymmetry )

protected

◆ SetLocation()

template<typename RealType >

void randlib::GeneralGeometricStableDistribution< RealType >::SetLocation ( double location )

protected

◆ SetParameters()

template<typename RealType >

void randlib::GeneralGeometricStableDistribution< RealType >::SetParameters	(	double	exponent,
		double	skewness,
		double	scale = `1.0`,
		double	location = `0.0`,
		double	shift = `0.`
	)

protected

◆ SetScale()

template<typename RealType >

void randlib::GeneralGeometricStableDistribution< RealType >::SetScale ( double scale )

protected

◆ SetShift()

template<typename RealType >

void randlib::GeneralGeometricStableDistribution< RealType >::SetShift ( double shift )

protected

◆ Skewness()

template<typename RealType >

long double randlib::GeneralGeometricStableDistribution< RealType >::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< RealType >.

◆ SupportType()

template<typename RealType >

Support randlib::GeneralGeometricStableDistribution< RealType >::SupportType ( ) const

overridevirtual

Returns: type of support

Implements randlib::UnivariateDistribution< RealType >.

◆ Variance()

template<typename RealType >

long double randlib::GeneralGeometricStableDistribution< RealType >::Variance ( ) const

overridevirtual

Returns: Variance of random variable

Implements randlib::UnivariateDistribution< RealType >.

Member Data Documentation

◆ alpha

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::alpha = 2

protected

characteristic exponent α

◆ alphaInv

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::alphaInv = 0.5

protected

◆ beta

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::beta = 0

protected

1/α

skewness β

◆ distributionType

template<typename RealType >

DISTRIBUTION_TYPE randlib::GeneralGeometricStableDistribution< RealType >::distributionType = LAPLACE

protected

type of distribution (Laplace by default)

◆ gamma

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::gamma = randlib::consts::sqrt2

protected

scale γ

◆ kappa

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::kappa = 1

protected

parameters for α = 2

asymmetry coefficient κ

◆ kappaInv

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::kappaInv = 1

protected

1 / κ

◆ kappaSq

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::kappaSq = 1

protected

κ^2

◆ log1pKappaSq

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::log1pKappaSq = randlib::consts::ln2

protected

log(1 + κ^2)

◆ logGamma

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::logGamma = 0.5 * randlib::consts::ln2

protected

log(γ)

◆ logKappa

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::logKappa = 0

protected

◆ m

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::m = 0

protected

shift m

◆ mu

template<typename RealType >

double randlib::GeneralGeometricStableDistribution< RealType >::mu = 0

protected

location μ

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

geometric_stable.hpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ DISTRIBUTION_TYPE

Constructor & Destructor Documentation

◆ GeneralGeometricStableDistribution()

◆ ~GeneralGeometricStableDistribution()

Member Function Documentation

◆ cdfLaplace()

◆ cdfLaplaceCompl()

◆ CFImpl()

◆ ExcessKurtosis()

◆ f()

◆ F()

◆ GetExponent()

◆ GetLogScale()

◆ GetScale()

◆ GetSkewness()

◆ logf()

◆ logpdfLaplace()

◆ MaxValue()

◆ Mean()

◆ Median()

◆ MinValue()

◆ Mode()

◆ operator()()

◆ pdfLaplace()

◆ quantileImpl()

◆ quantileImpl1m()

◆ quantileLaplace()

◆ quantileLaplace1m()

◆ searchTailQuantile()

◆ SetAsymmetry()

◆ SetLocation()

◆ SetParameters()

◆ SetScale()

◆ SetShift()

◆ Skewness()

◆ SupportType()

◆ Variance()

Member Data Documentation

◆ alpha

◆ alphaInv

◆ beta

◆ distributionType

◆ gamma

◆ kappa

◆ kappaInv

◆ kappaSq

◆ log1pKappaSq

◆ logGamma

◆ logKappa

◆ m

◆ mu