randlib Namespace Reference

Namespaces
namespace	consts
namespace	detail
namespace	legacy
	Engines of RandLib 1.x, kept for comparison with older results.
namespace	math
	Beta-related functions.

Classes
class	ArcsineRand
	The ArcsineRand class Arcsine distribution. More...
class	AsymmetricLaplaceDistribution
	The AsymmetricLaplaceDistribution class Abstract parent class for general Laplace and Asymmetric Laplace distributions. More...
class	AsymmetricLaplaceRand
	The AsymmetricLaplaceRand class Asymmetric Laplace distribution. More...
class	BaldingNicholsRand
	The BaldingNicholsRand class Balding-Nichols distribution. More...
class	BernoulliRand
	The BernoulliRand class Bernoulli distribution. More...
struct	BestFitResult
class	BetaBinomialRand
	The BetaBinomialRand class Beta-Binomial distribution. More...
class	BetaDistribution
	The BetaDistribution class Abstract class for Beta distribution. More...
class	BetaPrimeRand
	The BetaPrimeRand class Beta-prime distribution. More...
class	BetaRand
	The BetaRand class Beta distribution. More...
class	BinomialDistribution
	The BinomialDistribution class Abstract class for Binomial distribution. More...
class	BinomialRand
	The BinomialRand class Binomial distribution. More...
class	BivariateDistribution
	The BivariateDistribution class Abstract class for all bivariate probability distributions. More...
class	BivariateNormalRand
	The BivariateNormalRand class Bivariate Gaussian (normal) distribution. More...
class	CantorRand
	The CantorRand class Cantor distribution. More...
class	CategoricalRand
	The CategoricalRand class More...
class	CauchyRand
	The CauchyRand class Cauchy distribution. More...
struct	CensoredObservation
class	CenteredAsymmetricLaplaceRand
	The CenteredAsymmetricLaplaceRand class Centered Laplace distribution. More...
class	ChiRand
	The ChiRand class Chi distribution. More...
class	ChiSquaredRand
	The ChiSquaredRand class Chi-squared distribution. More...
class	CircularDistribution
	The CircularDistribution class Abstract class for all continuous circular distributions. More...
class	ContinuousBivariateDistribution
	The ContinuousBivariateDistribution class Abstract class for all bivariate probability distributions with marginal continuous distributions. More...
class	ContinuousDistribution
	The ContinuousDistribution class Abstract class for all continuous distributions. More...
struct	ContinuousGoodnessOfFit
class	DegenerateRand
	The DegenerateRand class Degenerate distribution. More...
class	DiscreteBivariateDistribution
	The DiscreteBivariateDistribution class Abstract class for all bivariate probability distributions with marginal discrete distributions. More...
class	DiscreteDistribution
	The DiscreteDistribution class Abstract class for all discrete distributions. More...
struct	DiscreteGoodnessOfFit
class	ErlangRand
	The ErlangRand class Erlang distibution. More...
class	ExponentialFamily
class	ExponentiallyModifiedGaussianRand
	The ExponentiallyModifiedGaussianRand class Exponentially-modified Gaussian distribution. More...
class	ExponentialRand
	The ExponentialRand class Exponential distribution. More...
class	FisherFRand
	The FisherFRand class F-distribution. More...
class	fit_error
	The fit_error class Thrown when a distribution cannot be fitted to a sample; code() tells why. More...
struct	FitOptions
struct	FitResult
class	FrechetRand
	The FrechetRand class Frechet distribution. More...
class	FreeRateGammaDistribution
	The FreeRateGammaDistribution class Abstract class for Gamma distribution with arbitrary scale/rate. More...
class	GammaDistribution
	The GammaDistribution class Abstract class for Gamma distribution. More...
class	GammaRand
	The GammaRand class Gamma distribution. More...
class	GeneralGeometricStableDistribution
	The GeneralGeometricStableDistribution class Abstract class for general interface of Asymmetric Laplace and Geometric-Stable distributions. More...
class	GeneralizedExtremeValueRand
class	GeneralizedParetoRand
class	GeometricRand
	The GeometricRand class Geometric distribution. More...
class	GeometricStableRand
	The GeometricStableRand class Geometric-Stable distribution. More...
class	GumbelRand
	The GumbelRand class Gumbel distribution. More...
class	HoltsmarkRand
	The HoltsmarkRand class Holtsmark distribution. More...
class	HyperGeometricRand
	The HyperGeometricRand class Hypergeometric distribution. More...
class	InverseGammaRand
	The InverseGammaRand class Inverse-Gamma distribution. More...
class	InverseGaussianRand
	The InverseGaussianRand class Inverse Gaussian (Wald) distribution. More...
class	IrwinHallRand
	The IrwinHallRand class Irwin-Hall distribution. More...
class	KolmogorovSmirnovRand
	The KolmogorovSmirnovRand class Kolmogorov-Smirnov distribution. More...
class	LandauRand
	The LandauRand class Landau distribution. More...
class	LaplaceRand
	The LaplaceRand class Laplace distribution. More...
class	LevyRand
	The LevyRand class Levy distribution. More...
class	LogarithmicRand
	The LogarithmicRand class Logarithmic distribution. More...
class	LogisticRand
	The LogisticRand class Logistic distribution. More...
class	LogNormalRand
	The LogNormalRand class Log-Normal distribution. More...
class	LogStableRand
	Exponential transform of a stable distribution. More...
class	MarchenkoPasturRand
	The MarchenkoPasturRand class Marchenko-Pastur distribution. More...
class	MaxwellBoltzmannRand
	The MaxwellBoltzmannRand class Maxwell-Boltzmann distribution. More...
class	NakagamiDistribution
	The NakagamiDistribution class Abstract class for Nakagami distribution. More...
class	NakagamiRand
	The NakagamiRand class Nakagami distribution. More...
class	NegativeBinomialDistribution
	The NegativeBinomialDistribution class Abstract class for Negative binomial distribution. More...
class	NegativeBinomialRand
	The NegativeBinomialRand class Negative binomial distribution. More...
class	NegativeHyperGeometricRand
	The NegativeHyperGeometricRand class Negative hypergeometric distribution. More...
class	NoncentralChiSquaredRand
	The NoncentralChiSquaredRand class Noncentral Chi-Squared distribution. More...
class	NoncentralTRand
	Noncentral Student's t-distribution. More...
class	NormalInverseGammaRand
	The NormalInverseGammaRand class Normal-inverse-gamma distribution. More...
class	NormalRand
	The NormalRand class Normal distribution. More...
class	not_implemented
	The not_implemented class Thrown when a quantity is not yet available for the given parameters, although the distribution itself is valid (for example, the stable density for exponents close to 1). More...
class	ParetoRand
	The ParetoRand class Pareto distribution. More...
class	Pcg32
	The Pcg32 class PCG-XSH-RR with 64 bits of state and 32-bit output (Melissa O'Neill, https://www.pcg-random.org), seeded exactly as the reference pcg32_srandom_r(seed, stream). More...
class	Pcg64
	The Pcg64 class PCG-XSL-RR with 128 bits of state and 64-bit output, the pcg64 engine of the reference C++ library and of NumPy, seeded as pcg64(seed, stream). More...
class	PlanckRand
	The PlanckRand class Planck distribution. More...
class	PoissonRand
	The PoissonRand class Poisson distribution. More...
class	ProbabilityDistribution
	The ProbabilityDistribution class Abstract class for all probability distributions. More...
class	RaabGreenRand
	The RaabGreenRand class Raab-Green distribution. More...
class	RademacherRand
	The RademacherRand class Rademacher distribution. More...
class	RaisedCosineDistribution
	The RaisedCosineDistribution class Abstract class for Raised-cosine distribution. More...
class	RaisedCosineRand
	The RaisedCosineRand class Raised-cosine distribution. More...
class	RayleighRand
	The RayleighRand class Rayleigh distribution. More...
class	RiceRand
	Rice distribution. More...
class	SechRand
	The SechRand class Hyperbolic secant distribution. More...
class	ShiftedAsymmetricLaplaceDistribution
	The ShiftedAsymmetricLaplaceDistribution class Abstract parent class for shifted Laplace and Asymmetric Laplace distributions. More...
class	SingularDistribution
	The SingularDistribution class Abstract class for all singular distributions. More...
class	SkellamRand
	The SkellamRand class Skellam distribution. More...
class	SplitMix64
	The SplitMix64 class Sebastiano Vigna's SplitMix64 generator. More...
class	StableCountRand
	Stable Count distribution. More...
class	StableDistribution
	The StableDistribution class Abstract class for Stable distribution. More...
class	StableRand
	The StableRand class Stable distribution. More...
class	StudentTRand
	The StudentTRand class Student's t-distribution. More...
struct	TailIndexEstimate
class	TriangularRand
	The TriangularRand class Triangular distribution. More...
class	TrinomialRand
	The TrinomialRand class Trinomial distribution. More...
class	UniformDiscreteRand
	The UniformDiscreteRand class Uniform discrete distribution. More...
class	UniformRand
	The UniformRand class Uniform continuous distribution. More...
class	UnivariateDistribution
	The UnivariateDistribution class Abstract class for all univariate probability distributions. More...
class	VonMisesRand
	The VonMisesRand class Von-Mises distribution. More...
class	WeibullRand
	The WeibullRand class Weibull distribution. More...
class	WignerSemicircleRand
	The WignerSemicircleRand class Wigner-Semicircle distribution. More...
class	WrappedExponentialRand
	The WrappedExponentialRand class Wrapped Exponential distribution. More...
class	Xoshiro256pp
	The Xoshiro256pp class xoshiro256++ 1.0 by David Blackman and Sebastiano Vigna: 256 bits of state, period 2^256 - 1. More...
class	YuleRand
	The YuleRand class Yule distribution. More...
class	ZetaRand
	The ZetaRand class Zeta distribution. More...
class	ZipfRand
	The ZipfRand class Zipf distribution. More...

Typedefs
template<typename T >
using	Pair = std::pair< T, T >
template<typename T >
using	Triplet = std::tuple< T, T, T >
using	IntPair = Pair< int >
using	DoublePair = Pair< double >
using	LongDoublePair = Pair< long double >
using	IntTriplet = Triplet< int >
using	DoubleTriplet = Triplet< double >
using	LongDoubleTriplet = Triplet< long double >
template<typename IntType = int>
using	PascalRand = NegativeBinomialRand< IntType, int >
template<typename IntType = int>
using	PolyaRand = NegativeBinomialRand< IntType, double >
using	DefaultEngine = Xoshiro256pp
	The engine used by default, including by the per-instance engines of the distributions.

Enumerations
enum class	FitErrorCode {   WrongSample , NotApplicable , WrongReturn , TooFewElements ,   WrongLevel , Undefined }
	Reason why a distribution could not be fitted to a sample. More...
enum class	Support { Finite , RightSemiFinite , LeftSemiFinite , Infinite }
	Shape of the support of a univariate distribution. More...
enum class	Censoring { Exact , Left , Right , Interval }
enum class	Method {   MLE , MethodOfMoments , UMVU , Bayes ,   Quantile }
enum class	Criterion { AIC , BIC }

Functions
double	stableTailQuantile (double p, bool upperTail, double alpha, double beta, double gamma, double mu)
	Quantile of the power-law tails of a stable law with α < 2: P(X > x) ~ C (1 + β) γ^α x^(-α) and P(X < -x) ~ C (1 - β) γ^α x^(-α) as x → ∞, with C = Γ(α) sin(πα/2) / π (1/π for α = 1).
std::uint64_t	random_seed ()
template<class Engine = DefaultEngine>
Engine	seed_from (std::seed_seq &sequence)
template<class Engine = DefaultEngine>
std::vector< Engine >	make_streams (std::uint64_t seed, std::size_t count)
	Engines for parallel simulations, one per thread: consecutive jump() calls for engines that have them (non-overlapping by construction), distinct PCG streams for Pcg32 and Pcg64, and seeds derived with SplitMix64 for any other engine.
template<class Distribution , class Prior > requires detail::ConjugateModel<Distribution, Prior>
auto	fit_bayes (std::span< const typename Distribution::value_type > sample, const Prior &prior)
template<class Distribution , std::ranges::contiguous_range Range, class Prior > requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::ConjugateModel<Distribution, Prior>
auto	fit_bayes (const Range &sample, const Prior &prior)
template<class Distribution , std::ranges::contiguous_range Range, class Prior , class Fixed > requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::ConditionalConjugateModel<Distribution, Prior, Fixed>
auto	fit_bayes (const Range &sample, const Prior &prior, Fixed fixed)
template<std::ranges::contiguous_range Range, std::floating_point Real> requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, Real>
auto	fit_bayes (const Range &sample, const NormalInverseGammaRand< Real > &prior)
template<std::ranges::contiguous_range Range, std::floating_point Real> requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, Real>
auto	fit_bayes (const Range &sample, const GammaRand< Real > &prior)
template<std::ranges::contiguous_range Range> requires std::integral<std::remove_cv_t<std::ranges::range_value_t<Range>>>
auto	fit_bayes (const Range &sample, const GammaRand< double > &prior)
template<class Distribution > requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution>
FitResult< Distribution >	fit_censored (std::span< const CensoredObservation< typename Distribution::value_type > > observations, FitOptions options={})
template<class Distribution , std::ranges::contiguous_range Range> requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, CensoredObservation<typename Distribution::value_type>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const CensoredObservation<typename Distribution::value_type>>>)
FitResult< Distribution >	fit_censored (const Range &observations, FitOptions options={})
template<class Distribution > requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution>
FitResult< Distribution >	fit_truncated (std::span< const typename Distribution::value_type > sample, typename Distribution::value_type lower, typename Distribution::value_type upper, FitOptions options={})
template<class Distribution , std::ranges::contiguous_range Range> requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const typename Distribution::value_type>>)
FitResult< Distribution >	fit_truncated (const Range &sample, typename Distribution::value_type lower, typename Distribution::value_type upper, FitOptions options={})
template<class Distribution > requires std::floating_point<typename Distribution::value_type>
ContinuousGoodnessOfFit	goodness_of_fit (const Distribution &distribution, std::span< const typename Distribution::value_type > sample)
template<class Distribution > requires std::integral<typename Distribution::value_type>
DiscreteGoodnessOfFit	goodness_of_fit (const Distribution &distribution, std::span< const typename Distribution::value_type > sample, int estimatedParameters=0)
template<class Distribution , std::ranges::contiguous_range Range> requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type>
auto	goodness_of_fit (const Distribution &distribution, const Range &sample)
template<class Distribution , std::ranges::contiguous_range Range> requires std::integral<typename Distribution::value_type> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type>
DiscreteGoodnessOfFit	goodness_of_fit (const Distribution &distribution, const Range &sample, int estimatedParameters)
template<class Distribution > requires detail::FittableModel<Distribution>
FitResult< Distribution >	fit (std::span< const typename Distribution::value_type > sample, FitOptions options={})
template<class Distribution > requires detail::FittableModel<Distribution>
FitResult< Distribution >	fit (std::span< const typename Distribution::value_type > sample, Method method)
template<class Distribution > requires detail::FittableModel<Distribution>
FitResult< Distribution >	fit_moments (std::span< const typename Distribution::value_type > sample)
template<class Distribution , std::ranges::contiguous_range Range> requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::FittableModel<Distribution>
FitResult< Distribution >	fit_moments (const Range &sample)
template<class First , class... Rest> requires (detail::FittableModel<First> && ... && detail::FittableModel<Rest>) && (std::same_as<typename First::value_type, typename Rest::value_type> && ...)
BestFitResult< First, Rest... >	fit_best (std::span< const typename First::value_type > sample, Criterion criterion)
template<class First , class... Rest, std::ranges::contiguous_range Range> requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename First::value_type> && (detail::FittableModel<First> && ... && detail::FittableModel<Rest>) && (std::same_as<typename First::value_type, typename Rest::value_type> && ...)
BestFitResult< First, Rest... >	fit_best (const Range &sample, Criterion criterion)
template<std::floating_point Real>
double	hill_estimator (std::span< const Real > sample, std::size_t order)
template<std::ranges::contiguous_range Range> requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)
double	hill_estimator (const Range &sample, std::size_t order)
template<std::floating_point Real>
std::vector< TailIndexEstimate >	hill_plot (std::span< const Real > sample, std::size_t maximumOrder=0)
template<std::ranges::contiguous_range Range> requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)
std::vector< TailIndexEstimate >	hill_plot (const Range &sample, std::size_t maximumOrder=0)
template<std::floating_point Real>
double	pickands_estimator (std::span< const Real > sample, std::size_t order)
template<std::ranges::contiguous_range Range> requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)
double	pickands_estimator (const Range &sample, std::size_t order)
template<std::floating_point Real>
FitResult< GeneralizedParetoRand< Real > >	fit_peaks_over_threshold (std::span< const Real > sample, Real threshold, FitOptions options={})
template<std::ranges::contiguous_range Range> requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)
auto	fit_peaks_over_threshold (const Range &sample, std::ranges::range_value_t< Range > threshold, FitOptions options={})

Typedef Documentation

DefaultEngine

using randlib::DefaultEngine = typedef Xoshiro256pp

The engine used by default, including by the per-instance engines of the distributions.

DoublePair

using randlib::DoublePair = typedef Pair<double>

DoubleTriplet

using randlib::DoubleTriplet = typedef Triplet<double>

IntPair

using randlib::IntPair = typedef Pair<int>

IntTriplet

using randlib::IntTriplet = typedef Triplet<int>

LongDoublePair

using randlib::LongDoublePair = typedef Pair<long double>

LongDoubleTriplet

using randlib::LongDoubleTriplet = typedef Triplet<long double>

Pair

template<typename T >

using randlib::Pair = typedef std::pair<T, T>

PascalRand

template<typename IntType = int>

using randlib::PascalRand = typedef NegativeBinomialRand<IntType, int>

PolyaRand

template<typename IntType = int>

using randlib::PolyaRand = typedef NegativeBinomialRand<IntType, double>

Triplet

template<typename T >

using randlib::Triplet = typedef std::tuple<T, T, T>

Enumeration Type Documentation

Censoring

enum class randlib::Censoring

strong

Enumerator
Exact
Left
Right
Interval

Criterion

enum class randlib::Criterion

strong

Enumerator
AIC
BIC

FitErrorCode

enum class randlib::FitErrorCode

strong

Reason why a distribution could not be fitted to a sample.

Enumerator
WrongSample	the sample could not have been drawn from this distribution
NotApplicable	the method cannot be applied to this distribution or sample
WrongReturn	the method returned invalid parameters
TooFewElements	the sample is too small
WrongLevel	the significance level is not in (0, 1)
Undefined	any other failure

Method

enum class randlib::Method

strong

Enumerator
MLE
MethodOfMoments
UMVU
Bayes
Quantile

Support

enum class randlib::Support

strong

Shape of the support of a univariate distribution.

Enumerator
Finite	[a, b]
RightSemiFinite	[a, ∞)
LeftSemiFinite	(-∞, b]
Infinite	(-∞, ∞)

Function Documentation

fit() [1/2]

template<class Distribution >
requires detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit	(	std::span< const typename Distribution::value_type >	sample,
		FitOptions	options = {}
	)

fit() [2/2]

template<class Distribution >
requires detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit	(	std::span< const typename Distribution::value_type >	sample,
		Method	method
	)

fit_bayes() [1/6]

template<std::ranges::contiguous_range Range>
requires std::integral<std::remove_cv_t<std::ranges::range_value_t<Range>>>

auto randlib::fit_bayes	(	const Range &	sample,
		const GammaRand< double > &	prior
	)

fit_bayes() [2/6]

template<std::ranges::contiguous_range Range, std::floating_point Real>
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, Real>

auto randlib::fit_bayes	(	const Range &	sample,
		const GammaRand< Real > &	prior
	)

fit_bayes() [3/6]

template<std::ranges::contiguous_range Range, std::floating_point Real>
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, Real>

auto randlib::fit_bayes	(	const Range &	sample,
		const NormalInverseGammaRand< Real > &	prior
	)

fit_bayes() [4/6]

template<class Distribution , std::ranges::contiguous_range Range, class Prior >
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::ConjugateModel<Distribution, Prior>

auto randlib::fit_bayes	(	const Range &	sample,
		const Prior &	prior
	)

fit_bayes() [5/6]

template<class Distribution , std::ranges::contiguous_range Range, class Prior , class Fixed >
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::ConditionalConjugateModel<Distribution, Prior, Fixed>

auto randlib::fit_bayes	(	const Range &	sample,
		const Prior &	prior,
		Fixed	fixed
	)

fit_bayes() [6/6]

template<class Distribution , class Prior >
requires detail::ConjugateModel<Distribution, Prior>

auto randlib::fit_bayes	(	std::span< const typename Distribution::value_type >	sample,
		const Prior &	prior
	)

fit_best() [1/2]

template<class First , class... Rest, std::ranges::contiguous_range Range>
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename First::value_type> && (detail::FittableModel<First> && ... && detail::FittableModel<Rest>) && (std::same_as<typename First::value_type, typename Rest::value_type> && ...)

BestFitResult< First, Rest... > randlib::fit_best	(	const Range &	sample,
		Criterion	criterion
	)

fit_best() [2/2]

template<class First , class... Rest>
requires (detail::FittableModel<First> && ... && detail::FittableModel<Rest>) && (std::same_as<typename First::value_type, typename Rest::value_type> && ...)

BestFitResult< First, Rest... > randlib::fit_best	(	std::span< const typename First::value_type >	sample,
		Criterion	criterion
	)

fit_censored() [1/2]

template<class Distribution , std::ranges::contiguous_range Range>
requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, CensoredObservation<typename Distribution::value_type>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const CensoredObservation<typename Distribution::value_type>>>)

FitResult< Distribution > randlib::fit_censored	(	const Range &	observations,
		FitOptions	options = {}
	)

fit_censored() [2/2]

template<class Distribution >
requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit_censored	(	std::span< const CensoredObservation< typename Distribution::value_type > >	observations,
		FitOptions	options = {}
	)

fit_moments() [1/2]

template<class Distribution , std::ranges::contiguous_range Range>
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit_moments

(

const Range &

sample

)

fit_moments() [2/2]

template<class Distribution >
requires detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit_moments

(

std::span< const typename Distribution::value_type >

sample

)

fit_peaks_over_threshold() [1/2]

template<std::ranges::contiguous_range Range>
requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)

auto randlib::fit_peaks_over_threshold	(	const Range &	sample,
		std::ranges::range_value_t< Range >	threshold,
		FitOptions	options = {}
	)

fit_peaks_over_threshold() [2/2]

template<std::floating_point Real>

FitResult< GeneralizedParetoRand< Real > > randlib::fit_peaks_over_threshold	(	std::span< const Real >	sample,
		Real	threshold,
		FitOptions	options = {}
	)

fit_truncated() [1/2]

template<class Distribution , std::ranges::contiguous_range Range>
requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const typename Distribution::value_type>>)

FitResult< Distribution > randlib::fit_truncated	(	const Range &	sample,
		typename Distribution::value_type	lower,
		typename Distribution::value_type	upper,
		FitOptions	options = {}
	)

fit_truncated() [2/2]

template<class Distribution >
requires std::floating_point<typename Distribution::value_type> && detail::FittableModel<Distribution>

FitResult< Distribution > randlib::fit_truncated	(	std::span< const typename Distribution::value_type >	sample,
		typename Distribution::value_type	lower,
		typename Distribution::value_type	upper,
		FitOptions	options = {}
	)

goodness_of_fit() [1/4]

template<class Distribution , std::ranges::contiguous_range Range>
requires std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type>

auto randlib::goodness_of_fit	(	const Distribution &	distribution,
		const Range &	sample
	)

goodness_of_fit() [2/4]

template<class Distribution , std::ranges::contiguous_range Range>
requires std::integral<typename Distribution::value_type> && std::same_as<std::remove_cv_t<std::ranges::range_value_t<Range>>, typename Distribution::value_type>

DiscreteGoodnessOfFit randlib::goodness_of_fit	(	const Distribution &	distribution,
		const Range &	sample,
		int	estimatedParameters
	)

goodness_of_fit() [3/4]

template<class Distribution >
requires std::floating_point<typename Distribution::value_type>

ContinuousGoodnessOfFit randlib::goodness_of_fit	(	const Distribution &	distribution,
		std::span< const typename Distribution::value_type >	sample
	)

goodness_of_fit() [4/4]

template<class Distribution >
requires std::integral<typename Distribution::value_type>

DiscreteGoodnessOfFit randlib::goodness_of_fit	(	const Distribution &	distribution,
		std::span< const typename Distribution::value_type >	sample,
		int	estimatedParameters = 0
	)

hill_estimator() [1/2]

template<std::ranges::contiguous_range Range>
requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)

double randlib::hill_estimator	(	const Range &	sample,
		std::size_t	order
	)

hill_estimator() [2/2]

template<std::floating_point Real>

double randlib::hill_estimator	(	std::span< const Real >	sample,
		std::size_t	order
	)

hill_plot() [1/2]

template<std::ranges::contiguous_range Range>
requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)

std::vector< TailIndexEstimate > randlib::hill_plot	(	const Range &	sample,
		std::size_t	maximumOrder = 0
	)

hill_plot() [2/2]

template<std::floating_point Real>

std::vector< TailIndexEstimate > randlib::hill_plot	(	std::span< const Real >	sample,
		std::size_t	maximumOrder = 0
	)

make_streams()

template<class Engine = DefaultEngine>

std::vector< Engine > randlib::make_streams	(	std::uint64_t	seed,
		std::size_t	count
	)

Engines for parallel simulations, one per thread: consecutive jump() calls for engines that have them (non-overlapping by construction), distinct PCG streams for Pcg32 and Pcg64, and seeds derived with SplitMix64 for any other engine.

Parameters

seed	common seed
count	number of engines

pickands_estimator() [1/2]

template<std::ranges::contiguous_range Range>
requires std::floating_point<std::remove_cv_t<std::ranges::range_value_t<Range>>> && (!std::same_as<std::remove_cvref_t<Range>, std::span<const std::remove_cv_t<std::ranges::range_value_t<Range>>>>)

double randlib::pickands_estimator	(	const Range &	sample,
		std::size_t	order
	)

pickands_estimator() [2/2]

template<std::floating_point Real>

double randlib::pickands_estimator	(	std::span< const Real >	sample,
		std::size_t	order
	)

random_seed()

std::uint64_t randlib::random_seed ( )

inline

Returns

non-deterministic 64-bit seed: std::random_device mixed with a high-resolution clock and the thread id through SplitMix64

seed_from()

template<class Engine = DefaultEngine>

Engine randlib::seed_from

(

std::seed_seq &

sequence

)

Parameters

sequence

seed sequence that fills the whole state of the engine

Returns

engine seeded from the sequence

stableTailQuantile()

double randlib::stableTailQuantile ( double  p, bool  upperTail, double  alpha, double  beta, double  gamma, double  mu  )

inline

Quantile of the power-law tails of a stable law with α < 2: P(X > x) ~ C (1 + β) γ^α x^(-α) and P(X < -x) ~ C (1 - β) γ^α x^(-α) as x → ∞, with C = Γ(α) sin(πα/2) / π (1/π for α = 1).

Geometric stable laws have the same tails.

Parameters

p	probability of the tail, small
upperTail	true for P(X > x) = p, false for P(X < x) = p
alpha	characteristic exponent
beta	skewness
gamma	scale
mu	location

Returns

asymptotic quantile, or NaN if that tail is not a power law