The NormalRand class
Normal distribution. More...

#include <normal.hpp>

Inheritance diagram for randlib::NormalRand< RealType >:

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Collaboration diagram for randlib::NormalRand< RealType >:

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Public Member Functions
	NormalRand (double location=0, double variance=1)

std::string	Name () const override

void	SetScale (double scale)

void	SetVariance (double variance)

double	GetScale () const noexcept

double	GetLogScale () const

double	GetPrecision () const

DoublePair	SufficientStatistic (RealType x) const override

DoublePair	SourceParameters () const override

DoublePair	SourceToNatural (DoublePair sourceParameters) const override

double	LogNormalizer (DoublePair theta) const override

DoublePair	LogNormalizerGradient (DoublePair theta) const override

double	CarrierMeasure (RealType) const override

double	f (const RealType &x) const override

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	Moment (size_t n) const

long double	ThirdMoment () const override

long double	FourthMoment () const override

void	FitLocation (std::span< const RealType > sample)
	set location, returned by maximium-likelihood estimator

void	FitLocation (std::span< const RealType > sample, DoublePair &confidenceInterval, double significanceLevel)
	set location, returned by maximium-likelihood estimator and return confidenceInterval for given significance level

void	FitVariance (std::span< const RealType > sample)
	set variance, returned by maximium-likelihood estimator

void	FitVariance (std::span< const RealType > sample, DoublePair &confidenceInterval, double significanceLevel, bool unbiased=false)

void	FitScale (std::span< const RealType > sample, bool unbiased=false)
	set scale, returned via maximum-likelihood estimation or unbiased estimator (which might be different from the unbiased estimator of variance)

void	Fit (std::span< const RealType > sample, bool unbiased=false)
	set parameters, returned by maximium-likelihood estimator if unbiased = false, otherwise set parameters via UMVU estimator

void	Fit (std::span< const RealType > sample, DoublePair &confidenceIntervalForMean, DoublePair &confidenceIntervalForVariance, double significanceLevel, bool unbiased=false)
	set parameters, returned by maximium-likelihood estimator if unbiased = false, otherwise set parameters via UMVU estimator, and return confidence intervals for given significance level

NormalRand< RealType >	FitLocationBayes (std::span< const RealType > sample, const NormalRand< RealType > &priorDistribution, bool MAP=false)
	set location, returned by bayesian estimation

InverseGammaRand< RealType >	FitVarianceBayes (std::span< const RealType > sample, const InverseGammaRand< RealType > &priorDistribution, bool MAP=false)
	set variance, returned by bayesian estimation

NormalInverseGammaRand< RealType >	FitBayes (std::span< const RealType > sample, const NormalInverseGammaRand< RealType > &priorDistribution, bool MAP=false)
	set parameters, returned by bayesian estimation

Public Member Functions inherited from randlib::StableDistribution< RealType >
virtual	~StableDistribution ()

Support	SupportType () const override

RealType	MinValue () const override

RealType	MaxValue () const override

void	SetLocation (double location)

void	SetScale (double scale)

void	SetParameterization (Parameterization value) noexcept

double	GetExponent () const noexcept

double	GetSkewness () const noexcept

double	GetScale () const noexcept

double	GetLocation () const noexcept

Parameterization	GetParameterization () const noexcept

double	GetLogScale () const noexcept

double	f (const RealType &x) const override

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	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

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

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< RealType, DoublePair >
	ExponentialFamily ()

virtual	~ExponentialFamily ()

virtual DoublePair	NaturalParameters () const

double	ProbabilityMeasure (RealType x) const

double	LogProbabilityMeasure (RealType x) const

double	KullbackLeiblerDivergence (DoublePair parameters) const

virtual double	CrossEntropyAdjusted (DoublePair parameters) const

virtual double	EntropyAdjusted () const

Static Public Member Functions
static NormalRand	FromMeanStd (double mean, double standardDeviation)

static NormalRand	FromMeanVariance (double mean, double variance)

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

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)

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

Protected Types inherited from randlib::StableDistribution< RealType >
enum class	Parameterization { S0 , S1 }
	Nolan parameterization used for the public location parameter. More...

Protected Member Functions inherited from randlib::StableDistribution< RealType >
	StableDistribution (double exponent, double skewness, double scale=1, double location=0, Parameterization selectedParameterization=Parameterization::S1)

void	SetParameters (double exponent, double skewness, double scale=1, double location=0)

double	pdfNormal (RealType x) const

double	logpdfNormal (RealType x) const

double	pdfCauchy (RealType x) const

double	logpdfCauchy (RealType x) const

double	pdfLevy (RealType x) const

double	logpdfLevy (RealType x) const

double	cdfNormal (RealType x) const

double	cdfNormalCompl (RealType x) const

double	cdfCauchy (RealType x) const

double	cdfCauchyCompl (RealType x) const

double	cdfLevy (RealType x) const

double	cdfLevyCompl (RealType x) const

RealType	quantileNormal (double p) const

RealType	quantileNormal1m (double p) const

RealType	quantileCauchy (double p) const

RealType	quantileCauchy1m (double p) const

RealType	quantileLevy (double p) const

RealType	quantileLevy1m (double p) const

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

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

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

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)

Protected Attributes inherited from randlib::StableDistribution< RealType >
double	alpha = 2
	characteristic exponent α

double	beta = 0
	skewness β

double	mu = 0
	location μ

double	gamma = randlib::consts::sqrt2
	scale γ

double	logGamma = 0.5 * randlib::consts::ln2
	log(γ)

double	pdfCoef
	hashed coefficient for faster pdf calculations

double	pdftailBound = INFINITY
	boundary k such that for \|x\| > k we can use pdf tail approximation

double	cdftailBound = INFINITY
	boundary k such that for \|x\| > k we can use cdf tail approximation

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::NormalRand< RealType >

The NormalRand class
Normal distribution.

f(x | μ, σ^2) = 1 / ((2 π σ^2)^(1/2) * exp(-(x - μ)^2 / (2 σ^2))

Notation: X ~ N(μ, σ^2)

Related distributions:
X ~ S(2, 0, σ/√2, μ)

Constructor & Destructor Documentation

◆ NormalRand()

template<typename RealType >

randlib::NormalRand< RealType >::NormalRand	(	double	location = `0`,
		double	variance = `1`
	)

Member Function Documentation

◆ CarrierMeasure()

template<typename RealType >

double randlib::NormalRand< RealType >::CarrierMeasure ( RealType ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ f()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: probability density function

Reimplemented from randlib::ContinuousDistribution< RealType >.

◆ F()

template<typename RealType >

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

override

◆ Fit() [1/2]

template<typename RealType >

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

set parameters, returned by maximium-likelihood estimator if unbiased = false, otherwise set parameters via UMVU estimator

Parameters

sample
unbiased

◆ Fit() [2/2]

template<typename RealType >

void randlib::NormalRand< RealType >::Fit	(	std::span< const RealType >	sample,
		DoublePair &	confidenceIntervalForMean,
		DoublePair &	confidenceIntervalForVariance,
		double	significanceLevel,
		bool	unbiased = `false`
	)

set parameters, returned by maximium-likelihood estimator if unbiased = false, otherwise set parameters via UMVU estimator, and return confidence intervals for given significance level

Parameters

sample
confidenceIntervalForMean
confidenceIntervalForVariance
significanceLevel
unbiased

calculate confidence interval for mean

calculate confidence interval for variance

◆ FitBayes()

template<typename RealType >

NormalInverseGammaRand< RealType > randlib::NormalRand< RealType >::FitBayes	(	std::span< const RealType >	sample,
		const NormalInverseGammaRand< RealType > &	priorDistribution,
		bool	MAP = `false`
	)

set parameters, returned by bayesian estimation

Parameters

sample
priorDistribution
MAP	if true, use MAP estimator

Returns: posterior distribution

◆ FitLocation() [1/2]

template<typename RealType >

void randlib::NormalRand< RealType >::FitLocation ( std::span< const RealType > sample )

set location, returned by maximium-likelihood estimator

Parameters

sample

◆ FitLocation() [2/2]

template<typename RealType >

void randlib::NormalRand< RealType >::FitLocation	(	std::span< const RealType >	sample,
		DoublePair &	confidenceInterval,
		double	significanceLevel
	)

set location, returned by maximium-likelihood estimator and return confidenceInterval for given significance level

Parameters

sample
confidenceInterval
significanceLevel

◆ FitLocationBayes()

template<typename RealType >

NormalRand< RealType > randlib::NormalRand< RealType >::FitLocationBayes	(	std::span< const RealType >	sample,
		const NormalRand< RealType > &	priorDistribution,
		bool	MAP = `false`
	)

set location, returned by bayesian estimation

Parameters

sample
priorDistribution
MAP	if true, use MAP estimator

Returns: posterior distribution

◆ FitScale()

template<typename RealType >

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

set scale, returned via maximum-likelihood estimation or unbiased estimator (which might be different from the unbiased estimator of variance)

Parameters

sample
unbiased

◆ FitVariance() [1/2]

template<typename RealType >

void randlib::NormalRand< RealType >::FitVariance ( std::span< const RealType > sample )

set variance, returned by maximium-likelihood estimator

Parameters

sample

◆ FitVariance() [2/2]

template<typename RealType >

void randlib::NormalRand< RealType >::FitVariance	(	std::span< const RealType >	sample,
		DoublePair &	confidenceInterval,
		double	significanceLevel,
		bool	unbiased = `false`
	)

Parameters

sample
confidenceInterval
significanceLevel
unbiased

◆ FitVarianceBayes()

template<typename RealType >

InverseGammaRand< RealType > randlib::NormalRand< RealType >::FitVarianceBayes	(	std::span< const RealType >	sample,
		const InverseGammaRand< RealType > &	priorDistribution,
		bool	MAP = `false`
	)

set variance, returned by bayesian estimation

Parameters

sample
priorDistribution
MAP	if true, use MAP estimator

Returns: posterior distribution

◆ FourthMoment()

template<typename RealType >

long double randlib::NormalRand< RealType >::FourthMoment ( ) const

inlineoverridevirtual

Returns: E[X^4]

Reimplemented from randlib::UnivariateDistribution< RealType >.

◆ FromMeanStd()

template<typename RealType >

static NormalRand randlib::NormalRand< RealType >::FromMeanStd	(	double	mean,
		double	standardDeviation
	)

inlinestatic

Parameters

mean	μ
standardDeviation	σ

Returns: N(μ, σ^2)

◆ FromMeanVariance()

template<typename RealType >

static NormalRand randlib::NormalRand< RealType >::FromMeanVariance	(	double	mean,
		double	variance
	)

inlinestatic

Parameters

mean	μ
variance	σ^2

Returns: N(μ, σ^2)

◆ GetLogScale()

template<typename RealType >

double randlib::NormalRand< RealType >::GetLogScale ( ) const

inline

Returns: log(σ)

◆ GetPrecision()

template<typename RealType >

double randlib::NormalRand< RealType >::GetPrecision ( ) const

inline

Returns: 1/σ^2

◆ GetScale()

template<typename RealType >

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

inlinenoexcept

Returns: σ

◆ logf()

template<typename RealType >

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

overridevirtual

Parameters

x

Returns: logarithm of probability density function

Implements randlib::ContinuousDistribution< RealType >.

◆ LogNormalizer()

template<typename RealType >

double randlib::NormalRand< RealType >::LogNormalizer ( DoublePair theta ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ LogNormalizerGradient()

template<typename RealType >

DoublePair randlib::NormalRand< RealType >::LogNormalizerGradient ( DoublePair theta ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ Moment()

template<typename RealType >

long double randlib::NormalRand< RealType >::Moment ( size_t n ) const

E[X^n] = Σ_{even k} C(n, k) μ^(n - k) σ^k (k - 1)!!

◆ Name()

template<typename RealType >

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

◆ S()

template<typename RealType >

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

override

◆ SetScale()

template<typename RealType >

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

◆ SetVariance()

template<typename RealType >

void randlib::NormalRand< RealType >::SetVariance ( double variance )

◆ SourceParameters()

template<typename RealType >

DoublePair randlib::NormalRand< RealType >::SourceParameters ( ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ SourceToNatural()

template<typename RealType >

DoublePair randlib::NormalRand< RealType >::SourceToNatural ( DoublePair sourceParameters ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ StandardVariate()

template<typename RealType >

template<std::uniform_random_bit_generator G>

RealType randlib::NormalRand< RealType >::StandardVariate ( G & g )

static

◆ SufficientStatistic()

template<typename RealType >

DoublePair randlib::NormalRand< RealType >::SufficientStatistic ( RealType x ) const

overridevirtual

Implements randlib::ExponentialFamily< RealType, DoublePair >.

◆ ThirdMoment()

template<typename RealType >

long double randlib::NormalRand< RealType >::ThirdMoment ( ) const

inlineoverridevirtual

Returns: E[X^3]

Reimplemented from randlib::UnivariateDistribution< RealType >.

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

normal.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NormalRand()

Member Function Documentation

◆ CarrierMeasure()

◆ f()

◆ F()

◆ Fit() [1/2]

◆ Fit() [2/2]

◆ FitBayes()

◆ FitLocation() [1/2]

◆ FitLocation() [2/2]

◆ FitLocationBayes()

◆ FitScale()

◆ FitVariance() [1/2]

◆ FitVariance() [2/2]

◆ FitVarianceBayes()

◆ FourthMoment()

◆ FromMeanStd()

◆ FromMeanVariance()

◆ GetLogScale()

◆ GetPrecision()

◆ GetScale()

◆ logf()

◆ LogNormalizer()

◆ LogNormalizerGradient()

◆ Moment()

◆ Name()

◆ operator()()

◆ S()

◆ SetScale()

◆ SetVariance()

◆ SourceParameters()

◆ SourceToNatural()

◆ StandardVariate()

◆ SufficientStatistic()

◆ ThirdMoment()