randlib::GammaDistribution< RealType > Class Template Reference

The GammaDistribution class
Abstract class for Gamma distribution. More...

#include <gamma.hpp>

Inheritance diagram for randlib::GammaDistribution< RealType >:

Collaboration diagram for randlib::GammaDistribution< RealType >:

Public Member Functions
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
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)

Static Public Member Functions
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)

Protected Member Functions
	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

Protected Attributes
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)

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

The GammaDistribution class
Abstract class for Gamma distribution.

f(x | α, β) = β^α / Γ(α) * x^(α-1) * exp(-βx), where Γ(α) denotes Gamma function

Notation X ~ Γ(α, β)

Related distributions:
σX ~ Γ(α, σβ)
If X ~ Γ(1, β), then X ~ Exp(β)
If X ~ Γ(0.5 * n, 0.5), then X ~ χ^2(n)
If X ~ Γ(k, β) for integer k, then X ~ Erlang(k, β)

Constructor & Destructor Documentation

GammaDistribution()

template<typename RealType >

randlib::GammaDistribution< RealType >::GammaDistribution ( double  shape, double  rate  )

protected

~GammaDistribution()

template<typename RealType >

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

inlinevirtual

Member Function Documentation

ExcessKurtosis()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns

probability density function

Reimplemented from randlib::ContinuousDistribution< RealType >.

F()

template<typename RealType >

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

override

GeometricMean()

template<typename RealType >

long double randlib::GammaDistribution< RealType >::GeometricMean

(

)

const

Returns

E[ln(X)]

GeometricVariance()

template<typename RealType >

long double randlib::GammaDistribution< RealType >::GeometricVariance

(

)

const

Returns

Var(ln(X))

GetDigammaShape()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetDigammaShape ( ) const

inlinenoexcept

Returns

ψ(α)

GetLogGammaShape()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetLogGammaShape ( ) const

inlinenoexcept

Returns

log(Γ(α))

GetLogRate()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetLogRate ( ) const

inlinenoexcept

Returns

log(β)

GetLogShape()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetLogShape ( ) const

inlinenoexcept

Returns

log(α)

GetRate()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetRate ( ) const

inlinenoexcept

Returns

β

GetScale()

template<typename RealType >

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

inlinenoexcept

Returns

θ = 1/β

GetShape()

template<typename RealType >

double randlib::GammaDistribution< RealType >::GetShape ( ) const

inlinenoexcept

Returns

α

logF()

template<typename RealType >

double randlib::GammaDistribution< RealType >::logF

(

const RealType &

x

)

const

logf()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns

logarithm of probability density function

Implements randlib::ContinuousDistribution< RealType >.

logS()

template<typename RealType >

double randlib::GammaDistribution< RealType >::logS

(

const RealType &

x

)

const

MaxValue()

template<typename RealType >

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

inlineoverridevirtual

Returns

maximum possible value that can be achieved by random variable

Implements randlib::ProbabilityDistribution< T >.

Mean()

template<typename RealType >

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

overridevirtual

Returns

E[X]

Implements randlib::UnivariateDistribution< RealType >.

Median()

template<typename RealType >

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

overridevirtual

Returns

such x that F(x) = 0.5

Reimplemented from randlib::UnivariateDistribution< RealType >.

MinValue()

template<typename RealType >

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

inlineoverridevirtual

Returns

minimum possible value that can be achieved by random variable

Implements randlib::ProbabilityDistribution< T >.

Mode()

template<typename RealType >

RealType randlib::GammaDistribution< 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::GammaDistribution< RealType >::operator()

(

G &

g

)

const

S()

template<typename RealType >

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

override

SetParameters()

template<typename RealType >

void randlib::GammaDistribution< RealType >::SetParameters ( double  shape, double  rate  )

protected

Parameters

shape	α
rate	β

set constants for generator

SetShape()

template<typename RealType >

void randlib::GammaDistribution< RealType >::SetShape ( double  shape )

protected

SetShape.

Parameters

shape

α

Skewness()

template<typename RealType >

long double randlib::GammaDistribution< 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 >.

StandardVariate()

template<typename RealType >

template<std::uniform_random_bit_generator G>

RealType randlib::GammaDistribution< RealType >::StandardVariate ( double  shape, G &  g  )

static

Parameters

shape	α
g	uniform random bit generator

Returns

gamma variate with shape α and unity rate

SupportType()

template<typename RealType >

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

inlineoverridevirtual

Returns

type of support

Implements randlib::UnivariateDistribution< RealType >.

Variance()

template<typename RealType >

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

overridevirtual

Returns

Var(X)

Implements randlib::UnivariateDistribution< RealType >.

Variate()

template<typename RealType >

template<std::uniform_random_bit_generator G>

RealType randlib::GammaDistribution< RealType >::Variate ( double  shape, double  rate, G &  g  )

static

Parameters

shape	α
rate	β
g	uniform random bit generator

Returns

gamma variate with shape α and rate β

Member Data Documentation

alpha

template<typename RealType >

double randlib::GammaDistribution< RealType >::alpha = 1

protected

shape α

beta

template<typename RealType >

double randlib::GammaDistribution< RealType >::beta = 1

protected

rate β

digammaAlpha

template<typename RealType >

double randlib::GammaDistribution< RealType >::digammaAlpha = -randlib::consts::egamma

protected

ψ(α)

lgammaAlpha

template<typename RealType >

double randlib::GammaDistribution< RealType >::lgammaAlpha = 0

protected

log(Γ(α))

logAlpha

template<typename RealType >

double randlib::GammaDistribution< RealType >::logAlpha = 0

protected

log(α)

logBeta

template<typename RealType >

double randlib::GammaDistribution< RealType >::logBeta = 0

protected

log(β)

pdfCoef

template<typename RealType >

double randlib::GammaDistribution< RealType >::pdfCoef = 0

protected

α * log(β) - log(Γ(α))

theta

template<typename RealType >

double randlib::GammaDistribution< RealType >::theta = 1

protected

scale θ = 1/β

---

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

• continuous/gamma.hpp