The ContinuousDistribution class
Abstract class for all continuous distributions. More...

#include <continuous.hpp>

Inheritance diagram for randlib::ContinuousDistribution< RealType >:

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Collaboration diagram for randlib::ContinuousDistribution< RealType >:

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Public Member Functions
virtual	~ContinuousDistribution ()

virtual double	f (const RealType &x) const

virtual double	logf (const RealType &x) const =0

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 ()

virtual Support	SupportType () const=0

bool	isLeftBounded () const

bool	isRightBounded () const

virtual long double	Mean () const=0

virtual long double	Variance () const=0

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 RealType	Median () const

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

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)

Protected Member Functions
	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 ()

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

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

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::ContinuousDistribution< RealType >

The ContinuousDistribution class
Abstract class for all continuous distributions.

Constructor & Destructor Documentation

◆ ContinuousDistribution()

template<typename RealType >

randlib::ContinuousDistribution< RealType >::ContinuousDistribution ( )

inlineprotected

◆ ~ContinuousDistribution()

template<typename RealType >

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

inlinevirtual

Member Function Documentation

◆ ExpectedValue()

template<typename RealType >

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

overrideprotectedvirtual

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)]

attempt to calculate expected value by numerical method use for distributions w/o explicit formula

Each side of the median is mapped by x = c ± s u / (1 - u) with the bulk scale s = 1 / f(c), so that a narrow peak far from the origin is resolved and infinite tails become finite intervals

Implements randlib::UnivariateDistribution< RealType >.

◆ f()

template<typename RealType >

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

inlinevirtual

Parameters

x

Returns: probability density function

◆ Hazard()

template<typename RealType >

double randlib::ContinuousDistribution< RealType >::Hazard ( const RealType & x ) const

overridevirtual

Parameters

x	input parameter

Returns: hazard function

0/1

0/0

Implements randlib::UnivariateDistribution< RealType >.

◆ integrateCharacteristicFunction()

template<typename RealType >

std::complex< double > randlib::ContinuousDistribution< RealType >::integrateCharacteristicFunction ( double t ) const

protected

Within δ = 1e-11 / t of the end a of the support e^{itx} = e^{ita} to that accuracy, so the mass there enters as F(a + δ) e^{ita}, whatever its singularity. The walk over half-periods starts where the remaining mass begins and stops when the survival function bounds the rest, so that a bulk many periods above the end of the support is not skipped as negligible

◆ KolmogorovSmirnovTest()

template<typename RealType >

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

Parameters

orderStatistic	sample sorted in ascending order
alpha	level of test

Returns: true if sample is from this distribution according to asymptotic KS-test, false otherwise

◆ LikelihoodFunction()

template<typename RealType >

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

overridevirtual

Parameters

sample

Returns: likelihood function for given sample

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ logf()

template<typename RealType >

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

pure virtual

Parameters

x

Returns: logarithm of probability density function

◆ LogLikelihoodFunction()

template<typename RealType >

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

overridevirtual

Parameters

sample

Returns: logarithm of likelihood function for given sample

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::UniformRand< RealType >.

◆ LogProbabilityDensityFunction()

template<typename RealType >

void randlib::ContinuousDistribution< RealType >::LogProbabilityDensityFunction	(	std::span< const RealType >	x,
		std::span< double >	y
	)		const

fill vector y with logf(x)

Parameters

x
y

◆ Mode()

template<typename RealType >

RealType randlib::ContinuousDistribution< 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.

good starting point

this shouldn't be nan or inf

Implements randlib::UnivariateDistribution< RealType >.

◆ ProbabilityDensityFunction()

template<typename RealType >

void randlib::ContinuousDistribution< RealType >::ProbabilityDensityFunction	(	std::span< const RealType >	x,
		std::span< double >	y
	)		const

fill vector y with f(x)

Parameters

x
y

◆ quantileImpl() [1/2]

template<typename RealType >

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

overrideprotectedvirtual

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::WrappedExponentialRand< RealType >, randlib::GeneralGeometricStableDistribution< RealType >, and randlib::NakagamiDistribution< RealType >.

◆ quantileImpl() [2/2]

template<typename RealType >

RealType randlib::ContinuousDistribution< RealType >::quantileImpl	(	double	p,
		RealType	initValue
	)		const

overrideprotectedvirtual

Parameters

p
initValue	initial value of x

Returns: such x that F(x) = p

Implements randlib::UnivariateDistribution< RealType >.

◆ quantileImpl1m() [1/2]

template<typename RealType >

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

overrideprotectedvirtual

Implements randlib::UnivariateDistribution< RealType >.

Reimplemented in randlib::WrappedExponentialRand< RealType >, randlib::GeneralGeometricStableDistribution< RealType >, and randlib::NakagamiDistribution< RealType >.

◆ quantileImpl1m() [2/2]

template<typename RealType >

RealType randlib::ContinuousDistribution< RealType >::quantileImpl1m	(	double	p,
		RealType	initValue
	)		const

overrideprotectedvirtual

Parameters

p
initValue	initial value of x

Returns: such x that F(x) = 1 - p

Implements randlib::UnivariateDistribution< RealType >.

◆ searchQuantile()

template<typename RealType >

RealType randlib::ContinuousDistribution< RealType >::searchQuantile	(	double	p,
		bool	upperTail,
		RealType	guess,
		double	relativeStep = `1e-3`
	)		const

protected

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.

It stops when the bracket cannot shrink in floating point.

Parameters

p	probability in (0, 1)
upperTail	search for S(x) = p instead of F(x) = p
guess	initial guess, or NaN
relativeStep	first step of the bracket expansion, relative to the guess

Returns: such x that F(x) = p (or S(x) = p)

Solve in the tail with the smaller probability: 1 - p is exact for p ≥ 1/2, and F (or S) cannot resolve a probability close to 1 as well as the other tail resolves 1 - p

g increases through zero at the quantile; for small p it is compared on a log scale

Bracket [a, b] with g(a) < 0 <= g(b), expanding geometrically from the guess, from a finite end of the support, or from 0

Bisection point: geometric in the distance to a finite support end while the bracket spans orders of magnitude, arithmetic otherwise

While the bracket spans orders of magnitude or g is infinite at an end, split it geometrically; then TOMS 748 refines it to full precision

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

continuous.hpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ContinuousDistribution()

◆ ~ContinuousDistribution()

Member Function Documentation

◆ ExpectedValue()

◆ f()

◆ Hazard()

◆ integrateCharacteristicFunction()

◆ KolmogorovSmirnovTest()

◆ LikelihoodFunction()

◆ logf()

◆ LogLikelihoodFunction()

◆ LogProbabilityDensityFunction()

◆ Mode()

◆ ProbabilityDensityFunction()

◆ quantileImpl() [1/2]

◆ quantileImpl() [2/2]

◆ quantileImpl1m() [1/2]

◆ quantileImpl1m() [2/2]

◆ searchQuantile()