The BernoulliRand class
Bernoulli distribution. More...

#include <bernoulli.hpp>

Inheritance diagram for randlib::BernoulliRand:

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Collaboration diagram for randlib::BernoulliRand:

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Public Member Functions
	BernoulliRand (double probability=0.5)

std::string	Name () const override

void	SetProbability (double probability)

double	P (const int &k) const override

double	logP (const int &k) const override

double	F (const int &k) const override

double	S (const int &k) const override

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

double	Entropy ()

Public Member Functions inherited from randlib::BinomialDistribution< int >
Support	SupportType () const override

int	MinValue () const override

int	MaxValue () const override

int	GetNumber () const noexcept

double	GetProbability () const noexcept

double	SufficientStatistic (int x) const override

double	SourceParameters () const override

double	SourceToNatural (double sourceParameters) const override

double	NaturalParameters () const override

double	LogNormalizer (double theta) const override

double	LogNormalizerGradient (double theta) const override

double	CarrierMeasure (int x) const override

double	EntropyAdjusted () const override

double	P (const int &k) const override

double	logP (const int &k) const override

double	F (const int &k) const override

double	S (const int &k) const override

int	operator() (G &g) const

long double	Mean () const override

long double	Variance () const override

int	Median () const override

int	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

double	GetLogFactorialN () const noexcept

double	GetLogProbability () const noexcept

double	GetLog1mProbability () const noexcept

void	FitProbability (std::span< const int > sample)
	Fit probability p with maximum-likelihood estimation.

BetaRand	FitProbabilityBayes (std::span< const int > sample, const BetaDistribution<> &priorDistribution, bool MAP=false)
	Fit probability p with prior assumption p ~ Beta(α, β)

BetaRand	FitProbabilityMinimax (std::span< const int > sample)
	Fit probability p with minimax estimator.

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)

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.

double	Hazard (const IntType &x) const override

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

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

Public Member Functions inherited from randlib::ExponentialFamily< T, P >
	ExponentialFamily ()

virtual	~ExponentialFamily ()

virtual P	SufficientStatistic (T x) const =0

virtual P	SourceToNatural (P sourceParameters) const =0

virtual double	LogNormalizer (P theta) const =0

virtual P	LogNormalizerGradient (P theta) const =0

virtual double	CarrierMeasure (T x) const =0

double	ProbabilityMeasure (T x) const

double	LogProbabilityMeasure (T x) const

double	KullbackLeiblerDivergence (P parameters) const

virtual double	CrossEntropyAdjusted (P parameters) const

Static Public Member Functions
template<std::uniform_random_bit_generator G>
static int	Variate (double probability, G &g)

template<std::uniform_random_bit_generator G>
static int	StandardVariate (G &g)

Static Public Member Functions inherited from randlib::BinomialDistribution< int >
static int	Variate (int number, double probability, 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::BinomialDistribution< int >
	BinomialDistribution (int number, double probability)

void	SetParameters (int number, double probability)

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

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

Protected Attributes inherited from randlib::BinomialDistribution< int >
double	p
	probability of success

double	q
	probability of failure

double	logProb
	log(p)

double	log1mProb
	log(q)

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 BernoulliRand class
Bernoulli distribution.

P(X = k) = p * 1_{k = 1} + (1 - p) * 1_{k = 0}

Notation: X ~ Bernoulli(p)

Related distributions:
X ~ Binomial(1, p)
X ~ Multin(1, 1 - p, p)
2X - 1 ~ Rademacher

Constructor & Destructor Documentation

◆ BernoulliRand()

randlib::BernoulliRand::BernoulliRand ( double probability = 0.5 )

inlineexplicit

Member Function Documentation

◆ Entropy()

double randlib::BernoulliRand::Entropy ( )

inline

◆ F()

double randlib::BernoulliRand::F ( const int & k ) const

inlineoverride

◆ logP()

double randlib::BernoulliRand::logP ( const int & k ) const

inlineoverride

◆ Name()

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

inlineoverridevirtual

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

Implements randlib::ProbabilityDistribution< T >.

◆ operator()()

template<std::uniform_random_bit_generator G>

int randlib::BernoulliRand::operator() ( G & g ) const

◆ P()

double randlib::BernoulliRand::P ( const int & k ) const

inlineoverride

◆ S()

double randlib::BernoulliRand::S ( const int & k ) const

inlineoverride

◆ SetProbability()

void randlib::BernoulliRand::SetProbability ( double probability )

inline

◆ StandardVariate()

template<std::uniform_random_bit_generator G>

int randlib::BernoulliRand::StandardVariate ( G & g )

static

◆ Variate()

template<std::uniform_random_bit_generator G>

int randlib::BernoulliRand::Variate	(	double	probability,
		G &	g
	)

static

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

bernoulli.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BernoulliRand()

Member Function Documentation

◆ Entropy()

◆ F()

◆ logP()

◆ Name()

◆ operator()()

◆ P()

◆ S()

◆ SetProbability()

◆ StandardVariate()

◆ Variate()