Classes
struct	BayesModel

struct	BayesModel< ExponentialRand< Real >, GammaRand< Real > >

struct	BayesModel< LogNormalRand< Real >, NormalInverseGammaRand< Real > >

struct	BayesModel< NormalRand< Real >, NormalInverseGammaRand< Real > >

struct	BayesModel< PoissonRand< Int >, GammaRand< double > >

struct	ChiSquaredBin

struct	ConditionalBayesModel

struct	ConditionalBayesModel< BinomialRand< Int >, BetaRand< double > >

struct	ConditionalBayesModel< LogNormalRand< Real >, InverseGammaRand< Real > >

struct	ConditionalBayesModel< LogNormalRand< Real >, NormalRand< Real > >

struct	ConditionalBayesModel< NegativeBinomialRand< Int, Shape >, BetaRand< double > >

struct	ConditionalBayesModel< NormalRand< Real >, InverseGammaRand< Real > >

struct	ConditionalBayesModel< NormalRand< Real >, NormalRand< Real > >

struct	ConditionalBayesModel< ParetoRand< Real >, GammaRand< Real > >

struct	ConditionalBayesModel< UniformRand< Real >, ParetoRand< Real > >

struct	ConditionalBayesModel< WeibullRand< Real >, InverseGammaRand< Real > >

class	EngineRef
	The EngineRef class Non-owning, type-erased reference to any uniform random bit generator. More...

struct	FitModel

struct	FitModel< ArcsineRand< Real > >

struct	FitModel< BernoulliRand >

struct	FitModel< BetaPrimeRand< Real > >

struct	FitModel< BetaRand< Real > >

struct	FitModel< BinomialRand< Int > >

struct	FitModel< CauchyRand< Real > >

struct	FitModel< ChiSquaredRand< Real > >

struct	FitModel< DegenerateRand >

struct	FitModel< ErlangRand< Real > >

struct	FitModel< ExponentialRand< Real > >

struct	FitModel< FisherFRand< Real > >

struct	FitModel< FrechetRand< Real > >

struct	FitModel< GammaRand< Real > >

struct	FitModel< GeneralizedExtremeValueRand< Real > >

struct	FitModel< GeneralizedParetoRand< Real > >

struct	FitModel< GeometricRand< Int > >

struct	FitModel< GumbelRand< Real > >

struct	FitModel< InverseGammaRand< Real > >

struct	FitModel< InverseGaussianRand< Real > >

struct	FitModel< LaplaceRand< Real > >

struct	FitModel< LevyRand< Real > >

struct	FitModel< LogisticRand< Real > >

struct	FitModel< LogNormalRand< Real > >

struct	FitModel< LogStableRand< Real > >

struct	FitModel< NegativeBinomialRand< Int, Shape > >

struct	FitModel< NoncentralChiSquaredRand< Real > >

struct	FitModel< NoncentralTRand< Real > >

struct	FitModel< NormalRand< Real > >

struct	FitModel< ParetoRand< Real > >

struct	FitModel< PoissonRand< Int > >

struct	FitModel< RayleighRand< Real > >

struct	FitModel< StableCountRand< Real > >

struct	FitModel< StableRand< Real > >

struct	FitModel< StudentTRand< Real > >

struct	FitModel< UniformDiscreteRand< Int > >

struct	FitModel< UniformRand< Real > >

struct	FitModel< WeibullRand< Real > >

struct	FitParameter

Concepts
concept	ConjugateModel

concept	ConditionalConjugateModel

concept	FittableModel

Typedefs
using	FixedParameterMap = std::map< std::string, double, std::less<> >

Functions
double	stableTanHalfPi (double alpha)

double	stableAtan (double value)

template<std::floating_point Real, std::uniform_random_bit_generator G>
Real	standardExponential (G &g)
	Ziggurat algorithm of Marsaglia and Tsang with 256 layers.

template<std::floating_point Real, std::uniform_random_bit_generator G>
Real	standardNormal (G &g)
	Ziggurat algorithm of Marsaglia and Tsang with 256 layers and an explicit sign bit.

template<typename IntType , std::uniform_random_bit_generator G>
IntType	poissonVariate (double rate, G &g)
	Poisson variate for a rate that changes from call to call, as in mixtures: the setup is a few elementary functions instead of the incomplete gamma function of PoissonRand.

long double	zetaTail (double exponent, long double firstTerm)

template<std::uniform_random_bit_generator G>
constexpr int	engineBits () noexcept
	Number of uniformly distributed bits in one output of G: floor(log2(max - min + 1))

template<std::uniform_random_bit_generator G>
std::uint64_t	randomBits (G &g, int count)

template<std::floating_point Real, std::uniform_random_bit_generator G>
Real	uniform01 (G &g)

template<std::floating_point Real, std::uniform_random_bit_generator G>
Real	uniform01Closed (G &g)
	k / (2^b - 1) for b = min(digits, 64) random bits: uniform on [0, 1]

template<std::floating_point Real, std::uniform_random_bit_generator G>
Real	uniform01HalfClosed (G &g)
	k / 2^b for b = min(digits, 64) random bits: uniform on [0, 1)

template<std::uniform_random_bit_generator G>
std::uint64_t	uniformBelow (G &g, std::uint64_t n)

double	andersonDarlingCdf (double statistic)

double	cvmCdfInfinite (double statistic)

double	cvmEd2 (double value)

double	cvmEd3 (double value)

double	cvmCorrectionTerm (int k, double statistic)

double	cvmCdf (double statistic, std::size_t sampleSize)

void	mergeSparseBins (std::vector< ChiSquaredBin > &bins)

double	toUnconstrained (double value, const FitParameter &parameter)

double	fromUnconstrained (double value, const FitParameter &parameter)

bool	withinBounds (double value, const FitParameter &parameter)

void	requireMethod (Method method, std::string_view distribution, std::initializer_list< Method > supported={Method::MLE, Method::MethodOfMoments})

template<class Distribution >
bool	requiresOptimization (Method method, const FixedParameterMap &fixed)

template<class T >
DoublePair	sampleMeanAndVariance (std::span< const T > sample)

template<class T >
double	sampleQuantile (std::span< const T > sample, double probability)

template<std::size_t Rows, std::size_t Columns>
double	bilinearInterpolation (const std::array< double, Rows > &rowGrid, const std::array< double, Columns > &columnGrid, const std::array< std::array< double, Columns >, Rows > &values, double row, double column)

std::optional< int >	fixedPositiveInteger (const FixedParameterMap &fixed, std::string_view name, std::string_view distribution)

std::vector< std::vector< double > >	inverse (std::vector< std::vector< double > > matrix)

template<class Distribution , class LogLikelihood >
double	negativeLogLikelihood (std::span< const double > parameters, const LogLikelihood &logLikelihood)

template<class Distribution , class Objective >
void	addUncertainty (FitResult< Distribution > &result, std::span< const FitParameter > specifications, const Objective &naturalObjective)

template<class Distribution , class LogLikelihood >
FitResult< Distribution >	fitLikelihood (std::span< const typename Distribution::value_type > initializationSample, FitOptions options, const LogLikelihood &logLikelihood, bool forceOptimization=false)

template<std::floating_point Real>
std::vector< Real >	sortedTailSample (std::span< const Real > sample)

template<std::floating_point Real>
double	hillFromSorted (std::span< const Real > sorted, std::size_t order)

Variables
constexpr std::size_t	MAX_ITER_REJECTION = 1000
	Upper bound on the iterations of rejection samplers; reaching it means there is a bug.

constexpr std::array< std::pair< long double, long double >, 257 >	normalZiggurat
	(exp(-x^2 / 2), x) at the layer boundaries of the normal ziggurat

constexpr std::array< std::pair< long double, long double >, 257 >	exponentialZiggurat
	(exp(-x), x) at the layer boundaries of the exponential ziggurat

Typedef Documentation

◆ FixedParameterMap

using randlib::detail::FixedParameterMap = typedef std::map<std::string, double, std::less<> >

Function Documentation

◆ addUncertainty()

template<class Distribution , class Objective >

void randlib::detail::addUncertainty	(	FitResult< Distribution > &	result,
		std::span< const FitParameter >	specifications,
		const Objective &	naturalObjective
	)

◆ andersonDarlingCdf()

double randlib::detail::andersonDarlingCdf ( double statistic )

inline

◆ bilinearInterpolation()

template<std::size_t Rows, std::size_t Columns>

double randlib::detail::bilinearInterpolation	(	const std::array< double, Rows > &	rowGrid,
		const std::array< double, Columns > &	columnGrid,
		const std::array< std::array< double, Columns >, Rows > &	values,
		double	row,
		double	column
	)

◆ cvmCdf()

double randlib::detail::cvmCdf	(	double	statistic,
		std::size_t	sampleSize
	)

inline

◆ cvmCdfInfinite()

double randlib::detail::cvmCdfInfinite ( double statistic )

inline

◆ cvmCorrectionTerm()

double randlib::detail::cvmCorrectionTerm	(	int	k,
		double	statistic
	)

inline

◆ cvmEd2()

double randlib::detail::cvmEd2 ( double value )

inline

◆ cvmEd3()

double randlib::detail::cvmEd3 ( double value )

inline

◆ engineBits()

template<std::uniform_random_bit_generator G>

constexpr int randlib::detail::engineBits ( )

constexprnoexcept

Number of uniformly distributed bits in one output of G: floor(log2(max - min + 1))

◆ fitLikelihood()

template<class Distribution , class LogLikelihood >

FitResult< Distribution > randlib::detail::fitLikelihood	(	std::span< const typename Distribution::value_type >	initializationSample,
		FitOptions	options,
		const LogLikelihood &	logLikelihood,
		bool	forceOptimization = `false`
	)

◆ fixedPositiveInteger()

std::optional< int > randlib::detail::fixedPositiveInteger	(	const FixedParameterMap &	fixed,
		std::string_view	name,
		std::string_view	distribution
	)

inline

◆ fromUnconstrained()

double randlib::detail::fromUnconstrained	(	double	value,
		const FitParameter &	parameter
	)

inline

◆ hillFromSorted()

template<std::floating_point Real>

double randlib::detail::hillFromSorted	(	std::span< const Real >	sorted,
		std::size_t	order
	)

◆ inverse()

std::vector< std::vector< double > > randlib::detail::inverse ( std::vector< std::vector< double > > matrix )

inline

◆ mergeSparseBins()

void randlib::detail::mergeSparseBins ( std::vector< ChiSquaredBin > & bins )

inline

◆ negativeLogLikelihood()

template<class Distribution , class LogLikelihood >

double randlib::detail::negativeLogLikelihood	(	std::span< const double >	parameters,
		const LogLikelihood &	logLikelihood
	)

◆ poissonVariate()

template<typename IntType , std::uniform_random_bit_generator G>

IntType randlib::detail::poissonVariate	(	double	rate,
		G &	g
	)

Poisson variate for a rate that changes from call to call, as in mixtures: the setup is a few elementary functions instead of the incomplete gamma function of PoissonRand.

Below rate 10 it inverts the distribution function with the probability recurrence; above, it uses the transformed rejection with squeeze PTRS of Hörmann (1993), whose expected number of iterations is bounded uniformly in the rate.

Parameters

rate	positive rate
g	engine

Returns: Poisson variate, saturated at the largest IntType

the tail beyond 1000 has probability below 1e-1400 for these rates; the bound only guards rounding

log P(x) through Stirling's series, free of the cancellation of x log(rate) and log(x!)

◆ randomBits()

template<std::uniform_random_bit_generator G>

std::uint64_t randlib::detail::randomBits	(	G &	g,
		int	count
	)

Parameters

g	any uniform random bit generator, including those whose range is not a power of two
count	number of bits, from 1 to 64

Returns: count independent uniform random bits, taken from the high end of the engine outputs

◆ requireMethod()

void randlib::detail::requireMethod	(	Method	method,
		std::string_view	distribution,
		std::initializer_list< Method >	supported = `{Method::MLE, Method::MethodOfMoments}`
	)

inline

◆ requiresOptimization()

template<class Distribution >

bool randlib::detail::requiresOptimization	(	Method	method,
		const FixedParameterMap &	fixed
	)

◆ sampleMeanAndVariance()

template<class T >

DoublePair randlib::detail::sampleMeanAndVariance ( std::span< const T > sample )

◆ sampleQuantile()

template<class T >

double randlib::detail::sampleQuantile	(	std::span< const T >	sample,
		double	probability
	)

◆ sortedTailSample()

template<std::floating_point Real>

std::vector< Real > randlib::detail::sortedTailSample ( std::span< const Real > sample )

◆ stableAtan()

double randlib::detail::stableAtan ( double value )

inline

◆ stableTanHalfPi()

double randlib::detail::stableTanHalfPi ( double alpha )

inline

◆ standardExponential()

template<std::floating_point Real, std::uniform_random_bit_generator G>

Real randlib::detail::standardExponential ( G & g )

Ziggurat algorithm of Marsaglia and Tsang with 256 layers.

Returns: Exp(1) variate

◆ standardNormal()

template<std::floating_point Real, std::uniform_random_bit_generator G>

Real randlib::detail::standardNormal ( G & g )

Ziggurat algorithm of Marsaglia and Tsang with 256 layers and an explicit sign bit.

Returns: N(0, 1) variate

Marsaglia's method for the tail beyond r: accept x if E > x^2 / 2

◆ toUnconstrained()

double randlib::detail::toUnconstrained	(	double	value,
		const FitParameter &	parameter
	)

inline

◆ uniform01()

template<std::floating_point Real, std::uniform_random_bit_generator G>

Real randlib::detail::uniform01 ( G & g )

Returns: (k + 1/2) / 2^b for b = digits - 1 random bits k: uniform on (0, 1) with the full resolution of Real, never 0 and never 1

◆ uniform01Closed()

template<std::floating_point Real, std::uniform_random_bit_generator G>

Real randlib::detail::uniform01Closed ( G & g )

k / (2^b - 1) for b = min(digits, 64) random bits: uniform on [0, 1]

◆ uniform01HalfClosed()

template<std::floating_point Real, std::uniform_random_bit_generator G>

Real randlib::detail::uniform01HalfClosed ( G & g )

k / 2^b for b = min(digits, 64) random bits: uniform on [0, 1)

◆ uniformBelow()

template<std::uniform_random_bit_generator G>

std::uint64_t randlib::detail::uniformBelow	(	G &	g,
		std::uint64_t	n
	)

Parameters

g	uniform random bit generator
n	positive number of outcomes

Returns: uniform integer in [0, n), without modulo bias: 64-bit values below 2^64 mod n are rejected

◆ withinBounds()

bool randlib::detail::withinBounds	(	double	value,
		const FitParameter &	parameter
	)

inline

◆ zetaTail()

long double randlib::detail::zetaTail	(	double	exponent,
		long double	firstTerm
	)

inline

Variable Documentation

◆ exponentialZiggurat

constexpr std::array<std::pair<long double, long double>, 257> randlib::detail::exponentialZiggurat

inlineconstexpr

(exp(-x), x) at the layer boundaries of the exponential ziggurat

◆ MAX_ITER_REJECTION

constexpr std::size_t randlib::detail::MAX_ITER_REJECTION = 1000

inlineconstexpr

Upper bound on the iterations of rejection samplers; reaching it means there is a bug.

◆ normalZiggurat

constexpr std::array<std::pair<long double, long double>, 257> randlib::detail::normalZiggurat

inlineconstexpr

(exp(-x^2 / 2), x) at the layer boundaries of the normal ziggurat

Classes

Concepts

Typedefs

Functions

Variables

Typedef Documentation

◆ FixedParameterMap

Function Documentation

◆ addUncertainty()

◆ andersonDarlingCdf()

◆ bilinearInterpolation()

◆ cvmCdf()

◆ cvmCdfInfinite()

◆ cvmCorrectionTerm()

◆ cvmEd2()

◆ cvmEd3()

◆ engineBits()

◆ fitLikelihood()

◆ fixedPositiveInteger()

◆ fromUnconstrained()

◆ hillFromSorted()

◆ inverse()

◆ mergeSparseBins()

◆ negativeLogLikelihood()

◆ poissonVariate()

◆ randomBits()

◆ requireMethod()

◆ requiresOptimization()

◆ sampleMeanAndVariance()

◆ sampleQuantile()

◆ sortedTailSample()

◆ stableAtan()

◆ stableTanHalfPi()

◆ standardExponential()

◆ standardNormal()

◆ toUnconstrained()

◆ uniform01()

◆ uniform01Closed()

◆ uniform01HalfClosed()

◆ uniformBelow()

◆ withinBounds()

◆ zetaTail()

Variable Documentation

◆ exponentialZiggurat

◆ MAX_ITER_REJECTION

◆ normalZiggurat