The RayleighRand class
Rayleigh distribution. More...

#include <nakagami.hpp>

Inheritance diagram for randlib::RayleighRand< RealType >:

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Collaboration diagram for randlib::RayleighRand< RealType >:

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Public Member Functions
	RayleighRand (double scale=1)
	RAYLEIGH.

std::string	Name () const override

void	SetScale (double scale)
	set scale σ

double	GetScale () const noexcept

double	f (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	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

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

Public Member Functions inherited from randlib::NakagamiDistribution< RealType >
Support	SupportType () const override

RealType	MinValue () const override

RealType	MaxValue () const override

double	GetShape () const noexcept

double	GetSpread () const noexcept

double	GetLogGammaFunction () const

double	GetLogGammaShapeRatio () const noexcept

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	FourthMoment () 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

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)

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)

Protected Member Functions inherited from randlib::NakagamiDistribution< RealType >
	NakagamiDistribution (double shape=0.5, double spread=1)

void	SetParameters (double shape, double spread)

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

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::RayleighRand< RealType >

The RayleighRand class
Rayleigh distribution.

Notation: X ~ Rayleigh(σ)

Related distributions: X / σ ~ χ(2) X ~ Nakagami(1, 2σ^2)

Constructor & Destructor Documentation

◆ RayleighRand()

template<typename RealType >

randlib::RayleighRand< RealType >::RayleighRand ( double scale = 1 )

explicit

RAYLEIGH.

Member Function Documentation

◆ ExcessKurtosis()

template<typename RealType >

long double randlib::RayleighRand< 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::NakagamiDistribution< RealType >.

◆ f()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: probability density function

Reimplemented from randlib::NakagamiDistribution< RealType >.

◆ F()

template<typename RealType >

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

override

◆ Fit()

template<typename RealType >

void randlib::RayleighRand< RealType >::Fit	(	std::span< const RealType >	sample,
		bool	unbiased = `false`
	)

fit scale via maximum-likelihood method if unbiased = false, otherwise set scale, returned by uniformly minimum variance unbiased estimator

Parameters

sample
unbiased	use the unbiased estimator instead of maximum likelihood

Sanity check

Calculate unbiased sigma

err ~ o(n^{-6.5}) < 1e-13

◆ GetScale()

template<typename RealType >

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

inlinenoexcept

Returns: scale σ

◆ Mean()

template<typename RealType >

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

overridevirtual

Returns: Mathematical expectation

Reimplemented from randlib::NakagamiDistribution< RealType >.

◆ Median()

template<typename RealType >

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

overridevirtual

Returns: such x that F(x) = 0.5

Reimplemented from randlib::NakagamiDistribution< RealType >.

◆ Mode()

template<typename RealType >

RealType randlib::RayleighRand< 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::NakagamiDistribution< RealType >.

◆ Name()

template<typename RealType >

std::string randlib::RayleighRand< 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::RayleighRand< RealType >::operator() ( G & g ) const

◆ S()

template<typename RealType >

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

override

◆ SetScale()

template<typename RealType >

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

set scale σ

Parameters

scale

◆ Skewness()

template<typename RealType >

long double randlib::RayleighRand< 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::NakagamiDistribution< RealType >.

◆ Variance()

template<typename RealType >

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

overridevirtual

Returns: Variance of random variable

Reimplemented from randlib::NakagamiDistribution< RealType >.

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

nakagami.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RayleighRand()

Member Function Documentation

◆ ExcessKurtosis()

◆ f()

◆ F()

◆ Fit()

◆ GetScale()

◆ Mean()

◆ Median()

◆ Mode()

◆ Name()

◆ operator()()

◆ S()

◆ SetScale()

◆ Skewness()

◆ Variance()