The DegenerateRand class
Degenerate distribution. More...

#include <degenerate.hpp>

Inheritance diagram for randlib::DegenerateRand:

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Collaboration diagram for randlib::DegenerateRand:

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Public Member Functions
	DegenerateRand (double value=0)

std::string	Name () const override

Support	SupportType () const override

double	MinValue () const override

double	MaxValue () const override

void	SetValue (double value)

double	GetValue () const noexcept

double	f (const double &x) const override

double	logf (const double &x) const override

double	F (const double &x) const override

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

long double	Mean () const override

long double	Variance () const override

double	Median () const override

double	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	Entropy () const

void	Fit (std::span< const double > sample)

Public Member Functions inherited from randlib::ContinuousDistribution< double >
virtual	~ContinuousDistribution ()

void	ProbabilityDensityFunction (std::span< const double > x, std::span< double > y) const
	fill vector y with f(x)

void	LogProbabilityDensityFunction (std::span< const double > x, std::span< double > y) const
	fill vector y with logf(x)

double	Hazard (const double &x) const override

double	LikelihoodFunction (std::span< const double > sample) const override

double	LogLikelihoodFunction (std::span< const double > sample) const override

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

Public Member Functions inherited from randlib::UnivariateDistribution< T >
virtual	~UnivariateDistribution ()

bool	isLeftBounded () const

bool	isRightBounded () const

T	Quantile (double p) const

T	Quantile1m (double p) const

void	QuantileFunction (std::span< const double > p, std::span< T > y) const

void	QuantileFunction1m (std::span< const double > p, std::span< T > y) const

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

void	CharacteristicFunction (std::span< const double > t, std::span< std::complex< double > > y) const

virtual double	Hazard (const T &x) const =0

void	HazardFunction (std::span< const T > 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

virtual double	LikelihoodFunction (std::span< const T > sample) const =0

virtual double	LogLikelihoodFunction (std::span< const T > sample) const =0

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< T >
static long double	GetSampleSum (std::span< const T > sample)

static long double	GetSampleMean (std::span< const T > sample)

static long double	GetSampleLogMean (std::span< const T > sample)

static long double	GetSampleVariance (std::span< const T > sample, double mean)

static long double	GetSampleLogVariance (std::span< const T > sample, double logMean)

static LongDoublePair	GetSampleMeanAndVariance (std::span< const T > sample)

static LongDoublePair	GetSampleLogMeanAndVariance (std::span< const T > sample)

static std::tuple< long double, long double, long double, long double >	GetSampleStatistics (std::span< const T > sample)

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

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

double	quantileImpl (double p, double initValue) const override

double	quantileImpl1m (double p, double initValue) const override

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

double	searchQuantile (double p, bool upperTail, double 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< T >
	UnivariateDistribution ()

virtual long double	ExpectedValue (const std::function< double(T)> &funPtr, T minPoint, T maxPoint) const =0

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< T >
static bool	allElementsAreNotGreaterThan (T value, std::span< const T > sample)

static bool	allElementsAreNotSmallerThan (T value, std::span< const T > sample)

static bool	allElementsAreNonNegative (std::span< const T > sample)

static bool	allElementsArePositive (std::span< const T > 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

The DegenerateRand class
Degenerate distribution.

f(x|a) = δ(a)

Notation: X ~ δ(a)

Constructor & Destructor Documentation

◆ DegenerateRand()

randlib::DegenerateRand::DegenerateRand ( double value = 0 )

inlineexplicit

Member Function Documentation

◆ Entropy()

long double randlib::DegenerateRand::Entropy ( ) const

inline

◆ ExcessKurtosis()

long double randlib::DegenerateRand::ExcessKurtosis ( ) const

inlineoverridevirtual

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< T >.

◆ f()

double randlib::DegenerateRand::f ( const double & x ) const

inlineoverridevirtual

Parameters

x

Returns: probability density function

Reimplemented from randlib::ContinuousDistribution< double >.

◆ F()

double randlib::DegenerateRand::F ( const double & x ) const

inlineoverride

◆ Fit()

void randlib::DegenerateRand::Fit ( std::span< const double > sample )

inline

Parameters

sample

◆ GetValue()

double randlib::DegenerateRand::GetValue ( ) const

inlinenoexcept

◆ logf()

double randlib::DegenerateRand::logf ( const double & x ) const

inlineoverridevirtual

Parameters

x

Returns: logarithm of probability density function

Implements randlib::ContinuousDistribution< double >.

◆ MaxValue()

double randlib::DegenerateRand::MaxValue ( ) const

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mean()

long double randlib::DegenerateRand::Mean ( ) const

inlineoverridevirtual

Returns: Mathematical expectation

Implements randlib::UnivariateDistribution< T >.

◆ Median()

double randlib::DegenerateRand::Median ( ) const

inlineoverridevirtual

Returns: such x that F(x) = 0.5

Reimplemented from randlib::UnivariateDistribution< T >.

◆ MinValue()

double randlib::DegenerateRand::MinValue ( ) const

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mode()

double randlib::DegenerateRand::Mode ( ) const

inlineoverridevirtual

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< double >.

◆ Name()

std::string randlib::DegenerateRand::Name ( ) const

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ operator()()

template<std::uniform_random_bit_generator G>

double randlib::DegenerateRand::operator() ( G & g ) const

◆ SetValue()

void randlib::DegenerateRand::SetValue ( double value )

inline

◆ Skewness()

long double randlib::DegenerateRand::Skewness ( ) const

inlineoverridevirtual

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< T >.

◆ SupportType()

Support randlib::DegenerateRand::SupportType ( ) const

inlineoverridevirtual

Returns: type of support

Implements randlib::UnivariateDistribution< T >.

◆ Variance()

long double randlib::DegenerateRand::Variance ( ) const

inlineoverridevirtual

Returns: Variance of random variable

Implements randlib::UnivariateDistribution< T >.

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

degenerate.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DegenerateRand()

Member Function Documentation

◆ Entropy()

◆ ExcessKurtosis()

◆ f()

◆ F()

◆ Fit()

◆ GetValue()

◆ logf()

◆ MaxValue()

◆ Mean()

◆ Median()

◆ MinValue()

◆ Mode()

◆ Name()

◆ operator()()

◆ SetValue()

◆ Skewness()

◆ SupportType()

◆ Variance()