The ExponentialRand class
Exponential distribution. More...

#include <exponential.hpp>

Inheritance diagram for randlib::ExponentialRand< RealType >:

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Collaboration diagram for randlib::ExponentialRand< RealType >:

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Public Member Functions
	ExponentialRand (double rate=1)

std::string	Name () const override

double	SufficientStatistic (RealType x) const override

double	SourceParameters () const override

double	SourceToNatural (double rate) const override

double	LogNormalizer (double theta) const override

double	LogNormalizerGradient (double theta) const override

double	CarrierMeasure (RealType) const override

double	CrossEntropyAdjusted (double rate) const override

double	EntropyAdjusted () const override

double	f (const RealType &x) const override

double	logf (const RealType &x) const override

double	F (const RealType &x) const override

double	S (const RealType &x) const override

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

long double	Entropy () const

long double	Moment (int n) const

long double	ThirdMoment () const override

long double	FourthMoment () const override

Public Member Functions inherited from randlib::FreeRateGammaDistribution< RealType >
void	SetRate (double rate)
	set rate β

void	SetScale (double scale)
	set scale θ = 1/β

void	FitRate (std::span< const RealType > sample, bool unbiased=false)
	set rate, estimated via maximum-likelihood method if unbiased = false, otherwise set rate, returned by uniformly minimum variance unbiased estimator

GammaRand< RealType >	FitRateBayes (std::span< const RealType > sample, const GammaDistribution< RealType > &priorDistribution, bool MAP=false)
	set rate, returned by bayesian estimation

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

Support	SupportType () const override

RealType	MinValue () const override

RealType	MaxValue () const override

double	GetShape () const noexcept

double	GetScale () const noexcept

double	GetRate () const noexcept

double	GetLogGammaShape () const noexcept

double	GetLogShape () const noexcept

double	GetDigammaShape () const noexcept

double	GetLogRate () const noexcept

double	f (const RealType &x) const override

double	logf (const RealType &x) const override

double	F (const RealType &x) const override

double	logF (const RealType &x) const

double	S (const RealType &x) const override

double	logS (const RealType &x) const

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

long double	Mean () const override

long double	GeometricMean () const

long double	Variance () const override

long double	GeometricVariance () const

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.

RealType	Median () const override

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

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< RealType, double >
	ExponentialFamily ()

virtual	~ExponentialFamily ()

virtual double	NaturalParameters () const

double	ProbabilityMeasure (RealType x) const

double	LogProbabilityMeasure (RealType x) const

double	KullbackLeiblerDivergence (double parameters) const

virtual double	CrossEntropyAdjusted (double parameters) const

Static Public Member Functions
static ExponentialRand	FromRate (double rate)

static ExponentialRand	FromScale (double scale)

template<std::uniform_random_bit_generator G>
static RealType	StandardVariate (G &g)

Static Public Member Functions inherited from randlib::GammaDistribution< RealType >
template<std::uniform_random_bit_generator G>
static RealType	StandardVariate (double shape, G &g)

template<std::uniform_random_bit_generator G>
static RealType	Variate (double shape, double rate, G &g)

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)

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

Protected Member Functions inherited from randlib::FreeRateGammaDistribution< RealType >
	FreeRateGammaDistribution (double shape, double rate)

Protected Member Functions inherited from randlib::GammaDistribution< RealType >
	GammaDistribution (double shape, double rate)

void	SetParameters (double shape, double rate)

void	SetShape (double shape)
	SetShape.

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

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

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

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)

Protected Attributes inherited from randlib::GammaDistribution< RealType >
double	alpha = 1
	shape α

double	beta = 1
	rate β

double	theta = 1
	scale θ = 1/β

double	lgammaAlpha = 0
	log(Γ(α))

double	pdfCoef = 0
	α * log(β) - log(Γ(α))

double	logAlpha = 0
	log(α)

double	logBeta = 0
	log(β)

double	digammaAlpha = -randlib::consts::egamma
	ψ(α)

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::ExponentialRand< RealType >

The ExponentialRand class
Exponential distribution.

f(x | β) = β exp(-βx)

Notation: X ~ Exp(β)

Related distributions:
X ~ Γ(1, β)

Constructor & Destructor Documentation

◆ ExponentialRand()

template<typename RealType >

randlib::ExponentialRand< RealType >::ExponentialRand ( double rate = 1 )

inlineexplicit

Member Function Documentation

◆ CarrierMeasure()

template<typename RealType >

double randlib::ExponentialRand< RealType >::CarrierMeasure ( RealType ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ CrossEntropyAdjusted()

template<typename RealType >

double randlib::ExponentialRand< RealType >::CrossEntropyAdjusted ( double rate ) const

override

◆ Entropy()

template<typename RealType >

long double randlib::ExponentialRand< RealType >::Entropy ( ) const

◆ EntropyAdjusted()

template<typename RealType >

double randlib::ExponentialRand< RealType >::EntropyAdjusted ( ) const

overridevirtual

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

◆ f()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: probability density function

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ F()

template<typename RealType >

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

override

◆ FourthMoment()

template<typename RealType >

long double randlib::ExponentialRand< RealType >::FourthMoment ( ) const

inlineoverridevirtual

Returns: E[X^4]

Reimplemented from randlib::UnivariateDistribution< RealType >.

◆ FromRate()

template<typename RealType >

static ExponentialRand randlib::ExponentialRand< RealType >::FromRate ( double rate )

inlinestatic

Returns: Exp(β) with rate β

◆ FromScale()

template<typename RealType >

static ExponentialRand randlib::ExponentialRand< RealType >::FromScale ( double scale )

inlinestatic

Returns: Exp(1/θ) with scale (mean) θ

◆ logf()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: logarithm of probability density function

Implements randlib::ContinuousDistribution< RealType >.

◆ LogNormalizer()

template<typename RealType >

double randlib::ExponentialRand< RealType >::LogNormalizer ( double theta ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ LogNormalizerGradient()

template<typename RealType >

double randlib::ExponentialRand< RealType >::LogNormalizerGradient ( double theta ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ Moment()

template<typename RealType >

long double randlib::ExponentialRand< RealType >::Moment ( int n ) const

◆ Name()

template<typename RealType >

std::string randlib::ExponentialRand< RealType >::Name ( ) const

overridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ operator()()

template<typename RealType >

template<std::uniform_random_bit_generator G>

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

◆ S()

template<typename RealType >

double randlib::ExponentialRand< RealType >::S ( const RealType & x ) const

override

◆ SourceParameters()

template<typename RealType >

double randlib::ExponentialRand< RealType >::SourceParameters ( ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ SourceToNatural()

template<typename RealType >

double randlib::ExponentialRand< RealType >::SourceToNatural ( double rate ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ StandardVariate()

template<typename RealType >

template<std::uniform_random_bit_generator G>

RealType randlib::ExponentialRand< RealType >::StandardVariate ( G & g )

static

◆ SufficientStatistic()

template<typename RealType >

double randlib::ExponentialRand< RealType >::SufficientStatistic ( RealType x ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, double >.

◆ ThirdMoment()

template<typename RealType >

long double randlib::ExponentialRand< RealType >::ThirdMoment ( ) const

inlineoverridevirtual

Returns: E[X^3]

Reimplemented from randlib::UnivariateDistribution< RealType >.

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

exponential.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ExponentialRand()

Member Function Documentation

◆ CarrierMeasure()

◆ CrossEntropyAdjusted()

◆ Entropy()

◆ EntropyAdjusted()

◆ f()

◆ F()

◆ FourthMoment()

◆ FromRate()

◆ FromScale()

◆ logf()

◆ LogNormalizer()

◆ LogNormalizerGradient()

◆ Moment()

◆ Name()

◆ operator()()

◆ S()

◆ SourceParameters()

◆ SourceToNatural()

◆ StandardVariate()

◆ SufficientStatistic()

◆ ThirdMoment()