The BetaDistribution class
Abstract class for Beta distribution. More...

#include <beta.hpp>

Inheritance diagram for randlib::BetaDistribution< RealType >:

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Collaboration diagram for randlib::BetaDistribution< RealType >:

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Public Member Functions
virtual	~BetaDistribution ()

Support	SupportType () const override

RealType	MinValue () const override

RealType	MaxValue () const override

double	GetAlpha () const noexcept

double	GetBeta () const noexcept

double	GetBetaFunction () const noexcept

double	GetLogBetaFunction () const noexcept

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	Mean () const override

long double	GeometricMean () const

long double	Variance () const override

long double	GeometricVariance () const

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

long double	MeanAbsoluteDeviation () const
	MeanAbsoluteDeviation.

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)

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.

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 Member Functions
	BetaDistribution (double shape1=1, double shape2=1, double minValue=0, double maxValue=1)

void	SetShapes (double shape1, double shape2)

void	SetSupport (double minValue, double maxValue)

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	quantileImpl (double p) const override

RealType	quantileImpl1m (double p, RealType initValue) const override

RealType	quantileImpl1m (double p) 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 = 1
	first shape α

double	beta = 1
	second shape β

double	a = 0
	min bound

double	b = 1
	max bound

double	bma = 1
	b-a

double	bmaInv = 1
	1/(b-a)

double	logbma = 0
	log(b-a)

GammaRand< RealType >	GammaRV1 {}

GammaRand< RealType >	GammaRV2 {}

Static Protected Attributes
static constexpr char	ALPHA_ZERO []

static constexpr char	BETA_ZERO []

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 "

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)

Detailed Description

template<typename RealType>
class randlib::BetaDistribution< RealType >

The BetaDistribution class
Abstract class for Beta distribution.

f(x | α, β) = y^{α-1} (1-y)^{β-1} / B(α, β),
where y = (x-a)/(b-a) and B(α, β) denotes Beta function

Notation: X ~ B(α, β, a, b) or X ~ B(α, β) for a=0 and b=1

Related distributions (a=0, b=1):
1 − X ~ B(β, α)
X / (1 - X) ~ B'(α, β)
X = Y / (Y + Z), where Y ~ Γ(α) and Z ~ Γ(β)
βX / α(1 - X) ~ F(2α, 2β)

Constructor & Destructor Documentation

◆ BetaDistribution()

template<typename RealType >

randlib::BetaDistribution< RealType >::BetaDistribution	(	double	shape1 = `1`,
		double	shape2 = `1`,
		double	minValue = `0`,
		double	maxValue = `1`
	)

protected

◆ ~BetaDistribution()

template<typename RealType >

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

inlinevirtual

Member Function Documentation

◆ CFImpl()

template<typename RealType >

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

overrideprotectedvirtual

Parameters

t

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

if we don't have singularity points, we can use direct integration

Reimplemented from randlib::UnivariateDistribution< RealType >.

◆ ExcessKurtosis()

template<typename RealType >

long double randlib::BetaDistribution< 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 >.

Reimplemented in randlib::UniformRand< RealType >.

◆ f()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: probability density function

Reimplemented from randlib::ContinuousDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ F()

template<typename RealType >

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

override

Standardize: distances to both ends are exact, unlike 1 minus the standardized value

Workaround known case

◆ GeometricMean()

template<typename RealType >

long double randlib::BetaDistribution< RealType >::GeometricMean ( ) const

Returns: E[ln(X)]

◆ GeometricVariance()

template<typename RealType >

long double randlib::BetaDistribution< RealType >::GeometricVariance ( ) const

Returns: Var(ln(X))

◆ GetAlpha()

template<typename RealType >

double randlib::BetaDistribution< RealType >::GetAlpha ( ) const

inlinenoexcept

Returns: first shape α

◆ GetBeta()

template<typename RealType >

double randlib::BetaDistribution< RealType >::GetBeta ( ) const

inlinenoexcept

Returns: second shape β

◆ GetBetaFunction()

template<typename RealType >

double randlib::BetaDistribution< RealType >::GetBetaFunction ( ) const

inlinenoexcept

Returns: B(α, β)

◆ GetLogBetaFunction()

template<typename RealType >

double randlib::BetaDistribution< RealType >::GetLogBetaFunction ( ) const

inlinenoexcept

Returns: log(B(α, β))

◆ logf()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: logarithm of probability density function

Implements randlib::ContinuousDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ MaxValue()

template<typename RealType >

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

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

Reimplemented in randlib::UniformRand< RealType >.

◆ Mean()

template<typename RealType >

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

overridevirtual

Returns: Mathematical expectation

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ MeanAbsoluteDeviation()

template<typename RealType >

long double randlib::BetaDistribution< RealType >::MeanAbsoluteDeviation ( ) const

MeanAbsoluteDeviation.

Returns: E[|X - E[X]|]

◆ Median()

template<typename RealType >

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

overridevirtual

Returns: such x that F(x) = 0.5

Reimplemented from randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ MinValue()

template<typename RealType >

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

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

Reimplemented in randlib::UniformRand< RealType >.

◆ Mode()

template<typename RealType >

RealType randlib::BetaDistribution< 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.

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ operator()()

template<typename RealType >

template<std::uniform_random_bit_generator G>

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

◆ quantileImpl()

template<typename RealType >

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

overrideprotectedvirtual

Implements randlib::UnivariateDistribution< RealType >.

◆ quantileImpl1m()

template<typename RealType >

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

overrideprotectedvirtual

Implements randlib::UnivariateDistribution< RealType >.

◆ S()

template<typename RealType >

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

override

Standardize: distances to both ends are exact, unlike 1 minus the standardized value

Workaround known case

◆ SetShapes()

template<typename RealType >

void randlib::BetaDistribution< RealType >::SetShapes	(	double	shape1,
		double	shape2
	)

protected

Parameters

shape1	α
shape2	β

◆ SetSupport()

template<typename RealType >

void randlib::BetaDistribution< RealType >::SetSupport	(	double	minValue,
		double	maxValue
	)

protected

Parameters

minValue	a
maxValue	b

◆ Skewness()

template<typename RealType >

long double randlib::BetaDistribution< 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 >.

Reimplemented in randlib::UniformRand< RealType >.

◆ SupportType()

template<typename RealType >

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

inlineoverridevirtual

Returns: type of support

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ Variance()

template<typename RealType >

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

overridevirtual

Returns: Variance of random variable

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

Member Data Documentation

◆ a

template<typename RealType >

double randlib::BetaDistribution< RealType >::a = 0

protected

min bound

◆ alpha

template<typename RealType >

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

protected

first shape α

◆ ALPHA_ZERO

template<typename RealType >

constexpr char randlib::BetaDistribution< RealType >::ALPHA_ZERO

staticconstexprprotected

Initial value:

=

"Possibly one or more elements of the sample coincide with the lower boundary a."

◆ b

template<typename RealType >

double randlib::BetaDistribution< RealType >::b = 1

protected

max bound

◆ beta

template<typename RealType >

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

protected

second shape β

◆ BETA_ZERO

template<typename RealType >

constexpr char randlib::BetaDistribution< RealType >::BETA_ZERO

staticconstexprprotected

Initial value:

=

"Possibly one or more elements of the sample coincide with the upper boundary b."

◆ bma

template<typename RealType >

double randlib::BetaDistribution< RealType >::bma = 1

protected

b-a

◆ bmaInv

template<typename RealType >

double randlib::BetaDistribution< RealType >::bmaInv = 1

protected

1/(b-a)

◆ GammaRV1

template<typename RealType >

GammaRand<RealType> randlib::BetaDistribution< RealType >::GammaRV1 {}

protected

◆ GammaRV2

template<typename RealType >

GammaRand<RealType> randlib::BetaDistribution< RealType >::GammaRV2 {}

protected

◆ logbma

template<typename RealType >

double randlib::BetaDistribution< RealType >::logbma = 0

protected

log(b-a)

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

continuous/beta.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BetaDistribution()

◆ ~BetaDistribution()

Member Function Documentation

◆ CFImpl()

◆ ExcessKurtosis()

◆ f()

◆ F()

◆ GeometricMean()

◆ GeometricVariance()

◆ GetAlpha()

◆ GetBeta()

◆ GetBetaFunction()

◆ GetLogBetaFunction()

◆ logf()

◆ MaxValue()

◆ Mean()

◆ MeanAbsoluteDeviation()

◆ Median()

◆ MinValue()

◆ Mode()

◆ operator()()

◆ quantileImpl()

◆ quantileImpl1m()

◆ S()

◆ SetShapes()

◆ SetSupport()

◆ Skewness()

◆ SupportType()

◆ Variance()

Member Data Documentation

◆ a

◆ alpha

◆ ALPHA_ZERO

◆ b

◆ beta

◆ BETA_ZERO

◆ bma

◆ bmaInv

◆ GammaRV1

◆ GammaRV2

◆ logbma