The UniformDiscreteRand class
Uniform discrete distribution. More...

#include <uniform_discrete.hpp>

Inheritance diagram for randlib::UniformDiscreteRand< IntType >:

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Collaboration diagram for randlib::UniformDiscreteRand< IntType >:

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Public Member Functions
	UniformDiscreteRand (IntType minValue=0, IntType maxValue=1)

std::string	Name () const override

Support	SupportType () const override

IntType	MinValue () const override

IntType	MaxValue () const override

void	SetBoundaries (IntType minValue, IntType maxValue)

double	P (const IntType &k) const override

double	logP (const IntType &k) const override

double	F (const IntType &k) const override

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

long double	Mean () const override

long double	Variance () const override

IntType	Median () const override

IntType	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

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

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

void	Fit (std::span< const IntType > sample)
	fit bounds via maximum-likelihood method

Public Member Functions inherited from randlib::DiscreteDistribution< IntType >
virtual	~DiscreteDistribution ()

void	ProbabilityMassFunction (std::span< const IntType > x, std::span< double > y) const
	fill vector y with P(x)

void	LogProbabilityMassFunction (std::span< const IntType > x, std::span< double > y) const
	fill vector y with logP(x)

double	Hazard (const IntType &x) const override

bool	PearsonChiSquaredTest (std::span< const IntType > orderStatistic, double alpha, int lowerBoundary, int upperBoundary, size_t numberOfEstimatedParameters=0) const

bool	PearsonChiSquaredTest (std::span< const IntType > orderStatistic, double alpha, size_t numberOfEstimatedParameters=0) const

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

bool	isLeftBounded () const

bool	isRightBounded () const

IntType	Quantile (double p) const

IntType	Quantile1m (double p) const

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

void	QuantileFunction1m (std::span< const double > p, std::span< IntType > 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 IntType > 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 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 IntType	StandardVariate (IntType minValue, IntType maxValue, G &g)

Static Public Member Functions inherited from randlib::UnivariateDistribution< IntType >
static long double	GetSampleSum (std::span< const IntType > sample)

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

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

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

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

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

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

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

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

Protected Member Functions inherited from randlib::DiscreteDistribution< IntType >
	DiscreteDistribution ()

IntType	quantileImpl (double p, IntType initValue) const override

IntType	quantileImpl (double p) const override

IntType	quantileImpl1m (double p, IntType initValue) const override

IntType	quantileImpl1m (double p) const override

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

Protected Member Functions inherited from randlib::UnivariateDistribution< IntType >
	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< IntType >
static bool	allElementsAreNotGreaterThan (IntType value, std::span< const IntType > sample)

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

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

static bool	allElementsArePositive (std::span< const IntType > 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 IntType>
class randlib::UniformDiscreteRand< IntType >

The UniformDiscreteRand class
Uniform discrete distribution.

Notation: X ~ U{a, ..., b}

P(X = k) = 1 / (b - a + 1) for a <= k <= b

Constructor & Destructor Documentation

◆ UniformDiscreteRand()

template<typename IntType >

randlib::UniformDiscreteRand< IntType >::UniformDiscreteRand	(	IntType	minValue = `0`,
		IntType	maxValue = `1`
	)

Member Function Documentation

◆ Entropy()

template<typename IntType >

long double randlib::UniformDiscreteRand< IntType >::Entropy ( ) const

◆ ExcessKurtosis()

template<typename IntType >

long double randlib::UniformDiscreteRand< IntType >::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< IntType >.

◆ F()

template<typename IntType >

double randlib::UniformDiscreteRand< IntType >::F ( const IntType & k ) const

override

◆ Fit()

template<typename IntType >

void randlib::UniformDiscreteRand< IntType >::Fit ( std::span< const IntType > sample )

fit bounds via maximum-likelihood method

Parameters

sample

◆ LikelihoodFunction()

template<typename IntType >

double randlib::UniformDiscreteRand< IntType >::LikelihoodFunction ( std::span< const IntType > sample ) const

overridevirtual

Parameters

sample

Returns: likelihood function of the distribution for given sample

Reimplemented from randlib::DiscreteDistribution< IntType >.

◆ LogLikelihoodFunction()

template<typename IntType >

double randlib::UniformDiscreteRand< IntType >::LogLikelihoodFunction ( std::span< const IntType > sample ) const

overridevirtual

Parameters

sample

Returns: log-likelihood function of the distribution for given sample

Reimplemented from randlib::DiscreteDistribution< IntType >.

◆ logP()

template<typename IntType >

double randlib::UniformDiscreteRand< IntType >::logP ( const IntType & x ) const

overridevirtual

Parameters

x

Returns: logarithm of probability to get x

Implements randlib::DiscreteDistribution< IntType >.

◆ MaxValue()

template<typename IntType >

IntType randlib::UniformDiscreteRand< IntType >::MaxValue ( ) const

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mean()

template<typename IntType >

long double randlib::UniformDiscreteRand< IntType >::Mean ( ) const

overridevirtual

Returns: Mathematical expectation

Implements randlib::UnivariateDistribution< IntType >.

◆ Median()

template<typename IntType >

IntType randlib::UniformDiscreteRand< IntType >::Median ( ) const

overridevirtual

Returns: such x that F(x) = 0.5

Reimplemented from randlib::UnivariateDistribution< IntType >.

◆ MinValue()

template<typename IntType >

IntType randlib::UniformDiscreteRand< IntType >::MinValue ( ) const

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ Mode()

template<typename IntType >

IntType randlib::UniformDiscreteRand< IntType >::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.

this can be any value in [a, b]

Works only for unimodal distributions

Reimplemented from randlib::DiscreteDistribution< IntType >.

◆ Name()

template<typename IntType >

std::string randlib::UniformDiscreteRand< IntType >::Name ( ) const

overridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ operator()()

template<typename IntType >

template<std::uniform_random_bit_generator G>

IntType randlib::UniformDiscreteRand< IntType >::operator() ( G & g ) const

◆ P()

template<typename IntType >

double randlib::UniformDiscreteRand< IntType >::P ( const IntType & k ) const

overridevirtual

Parameters

k

Returns: probability to get k

Reimplemented from randlib::DiscreteDistribution< IntType >.

◆ SetBoundaries()

template<typename IntType >

void randlib::UniformDiscreteRand< IntType >::SetBoundaries	(	IntType	minValue,
		IntType	maxValue
	)

◆ Skewness()

template<typename IntType >

long double randlib::UniformDiscreteRand< IntType >::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< IntType >.

◆ StandardVariate()

template<typename IntType >

template<std::uniform_random_bit_generator G>

IntType randlib::UniformDiscreteRand< IntType >::StandardVariate	(	IntType	minValue,
		IntType	maxValue,
		G &	g
	)

static

◆ SupportType()

template<typename IntType >

Support randlib::UniformDiscreteRand< IntType >::SupportType ( ) const

inlineoverridevirtual

Returns: type of support

Implements randlib::UnivariateDistribution< IntType >.

◆ Variance()

template<typename IntType >

long double randlib::UniformDiscreteRand< IntType >::Variance ( ) const

overridevirtual

Returns: Variance of random variable

Implements randlib::UnivariateDistribution< IntType >.

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

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ UniformDiscreteRand()

Member Function Documentation

◆ Entropy()

◆ ExcessKurtosis()

◆ F()

◆ Fit()

◆ LikelihoodFunction()

◆ LogLikelihoodFunction()

◆ logP()

◆ MaxValue()

◆ Mean()

◆ Median()

◆ MinValue()

◆ Mode()

◆ Name()

◆ operator()()

◆ P()

◆ SetBoundaries()

◆ Skewness()

◆ StandardVariate()

◆ SupportType()

◆ Variance()