npstat::AbsDistribution1D Struct Reference

#include <AbsDistribution1D.hh>

Inheritance diagram for npstat::AbsDistribution1D:

Public Member Functions
virtual double	density (double x) const =0
virtual double	cdf (double x) const =0
virtual double	exceedance (double x) const =0
virtual double	quantile (double x) const =0
bool	operator== (const AbsDistribution1D &r) const
bool	operator!= (const AbsDistribution1D &r) const
virtual AbsDistribution1D *	clone () const =0
virtual unsigned	random (AbsRandomGenerator &g, double *generatedRandom) const
long double	empiricalMoment (long double center, unsigned order, unsigned nIntegrationPoints=1024U, bool useFejerQuadrature=false) const
template<class Functor >
double	expectation (const Functor &fcn, unsigned nIntegrationPoints=1024U, bool useFejerQuadrature=false) const
virtual gs::ClassId	classId () const =0
virtual bool	write (std::ostream &) const

Static Public Member Functions
static const char *	classname ()
static unsigned	version ()
static AbsDistribution1D *	read (const gs::ClassId &id, std::istream &)

Protected Member Functions
virtual bool	isEqual (const AbsDistribution1D &) const =0

Detailed Description

All classes derived from this base should have copy constructors (possibly automatic).

quantile(0.0) and quantile(1.0) should return the boundaries of the support interval.

Member Function Documentation

cdf()

virtual double npstat::AbsDistribution1D::cdf ( double  x ) const

pure virtual

Cumulative distribution function

Implemented in npstat::VerticallyInterpolatedDistribution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::LeftCensoredDistribution, npstat::InterpolatedDistribution1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::DistributionMix1D, npstat::ModulatedDistribution1D< Functor >, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::CompositeDistribution1D, npstat::AbsScalableDistribution1D, and npstat::ComparisonDistribution1D.

classId()

virtual gs::ClassId npstat::AbsDistribution1D::classId ( ) const

pure virtual

Prototype needed for I/O

Implemented in npstat::AbsScalableDistribution1D, npstat::VerticallyInterpolatedDistribution1D, npstat::UGaussConvolution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::QuantileTable1D, npstat::PowerRatio1D, npstat::PowerHalfCauchy1D, npstat::PolynomialDistro1D, npstat::ModulatedDistribution1D< Functor >, npstat::LocationScaleFamily1D, npstat::LegendreDistro1D, npstat::LeftCensoredDistribution, npstat::JohnsonSystem, npstat::JohnsonSb, npstat::JohnsonSu, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::InterpolatedDistribution1D, npstat::GaussianMixture1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::BinnedDensity1D, npstat::Tabulated1D, npstat::StudentsT1D, npstat::Moyal1D, npstat::LogNormal, npstat::Cauchy1D, npstat::Huber1D, npstat::UniPareto1D, npstat::Pareto1D, npstat::Gamma1D, npstat::Beta1D, npstat::SymmetricBeta1D, npstat::BifurcatedGauss1D, npstat::MirroredGauss1D, npstat::TruncatedGauss1D, npstat::Gauss1D, npstat::LogQuadratic1D, npstat::Quadratic1D, npstat::Logistic1D, npstat::Laplace1D, npstat::Exponential1D, npstat::IsoscelesTriangle1D, npstat::Uniform1D, npstat::DistributionMix1D, npstat::DeltaMixture1D, npstat::CompositeDistribution1D, npstat::ComparisonDistribution1D, and npstat::ChebyshevDistro1D.

clone()

virtual AbsDistribution1D* npstat::AbsDistribution1D::clone ( ) const

pure virtual

"Virtual copy constructor"

Implemented in npstat::AbsInterpolatedDistribution1D, npstat::AbsScalableDistribution1D, npstat::VerticallyInterpolatedDistribution1D, npstat::UGaussConvolution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::QuantileTable1D, npstat::PowerRatio1D, npstat::PowerHalfCauchy1D, npstat::PolynomialDistro1D, npstat::ModulatedDistribution1D< Functor >, npstat::LocationScaleFamily1D, npstat::LegendreDistro1D, npstat::LeftCensoredDistribution, npstat::JohnsonSystem, npstat::JohnsonSb, npstat::JohnsonSu, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::InterpolatedDistribution1D, npstat::GaussianMixture1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::BinnedDensity1D, npstat::Tabulated1D, npstat::StudentsT1D, npstat::Moyal1D, npstat::LogNormal, npstat::Cauchy1D, npstat::Huber1D, npstat::UniPareto1D, npstat::Pareto1D, npstat::Gamma1D, npstat::Beta1D, npstat::SymmetricBeta1D, npstat::BifurcatedGauss1D, npstat::MirroredGauss1D, npstat::TruncatedGauss1D, npstat::Gauss1D, npstat::LogQuadratic1D, npstat::Quadratic1D, npstat::Logistic1D, npstat::Laplace1D, npstat::Exponential1D, npstat::IsoscelesTriangle1D, npstat::Uniform1D, npstat::DistributionMix1D, npstat::DeltaMixture1D, npstat::JohnsonLadder, npstat::BinnedCompositeJohnson, npstat::LogQuadraticLadder, npstat::BetaGauss1D, npstat::CompositeGauss1D, npstat::CompositeDistribution1D, npstat::ComparisonDistribution1D, and npstat::ChebyshevDistro1D.

density()

virtual double npstat::AbsDistribution1D::density ( double  x ) const

pure virtual

Probability density

Implemented in npstat::VerticallyInterpolatedDistribution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::LeftCensoredDistribution, npstat::InterpolatedDistribution1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::DistributionMix1D, npstat::ModulatedDistribution1D< Functor >, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::CompositeDistribution1D, npstat::AbsScalableDistribution1D, and npstat::ComparisonDistribution1D.

empiricalMoment()

long double npstat::AbsDistribution1D::empiricalMoment	(	long double	center,
		unsigned	order,
		unsigned	nIntegrationPoints = 1024U,
		bool	useFejerQuadrature = false
	)		const

Numerical moment calculation using Gauss-Legendre or Fejer quadrature. If "useFejerQuadrature" argument is set to "false", the number of integration points should be supported by the "GaussLegendreQuadrature" class.

No attempt is made to determine whether the moment actually exists. If it does not, the function might return Inf or fail in some other ways. This method might also be highly inaccurate for distributions with singularities or for distributions that have a lot of weight near support boundaries.

For better results, it might be useful to calculate the 0th order moment (i.e., the normalization factor for the quadrature scheme chosen) and then divide everything by it.

exceedance()

virtual double npstat::AbsDistribution1D::exceedance ( double  x ) const

pure virtual

1 - cdf, known as "survival function" or "exceedance". Implementations should avoid subtractive cancellation.

Implemented in npstat::VerticallyInterpolatedDistribution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::LeftCensoredDistribution, npstat::InterpolatedDistribution1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::DistributionMix1D, npstat::ModulatedDistribution1D< Functor >, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::CompositeDistribution1D, npstat::AbsScalableDistribution1D, and npstat::ComparisonDistribution1D.

expectation()

template<class Functor >

double npstat::AbsDistribution1D::expectation	(	const Functor &	fcn,
		unsigned	nIntegrationPoints = 1024U,
		bool	useFejerQuadrature = false
	)		const

Numerical calculation of the expectation value of some functor, using Gauss-Legendre or Fejer quadrature. If "useFejerQuadrature" argument is set to "false", the number of integration points should be supported by the "GaussLegendreQuadrature" class.

isEqual()

virtual bool npstat::AbsDistribution1D::isEqual ( const AbsDistribution1D &  ) const

protectedpure virtual

Comparison for equality. To be implemented by derived classes.

Implemented in npstat::RatioOfNormals, npstat::QuantileTable1D, npstat::GaussianMixture1D, npstat::Moyal1D, npstat::Cauchy1D, npstat::Gauss1D, npstat::Logistic1D, npstat::Laplace1D, npstat::Exponential1D, npstat::IsoscelesTriangle1D, npstat::Uniform1D, npstat::ModulatedDistribution1D< Functor >, npstat::LocationScaleFamily1D, npstat::AbsScalableDistribution1D, npstat::VerticallyInterpolatedDistribution1D, npstat::UGaussConvolution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::PowerRatio1D, npstat::PowerHalfCauchy1D, npstat::PolynomialDistro1D, npstat::LegendreDistro1D, npstat::LeftCensoredDistribution, npstat::JohnsonSystem, npstat::JohnsonSb, npstat::JohnsonSu, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::InterpolatedDistribution1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::BinnedDensity1D, npstat::Tabulated1D, npstat::StudentsT1D, npstat::LogNormal, npstat::Huber1D, npstat::UniPareto1D, npstat::Pareto1D, npstat::Gamma1D, npstat::Beta1D, npstat::SymmetricBeta1D, npstat::BifurcatedGauss1D, npstat::MirroredGauss1D, npstat::TruncatedGauss1D, npstat::LogQuadratic1D, npstat::Quadratic1D, npstat::DistributionMix1D, npstat::DeltaMixture1D, npstat::CompositeDistribution1D, npstat::ComparisonDistribution1D, and npstat::ChebyshevDistro1D.

operator!=()

bool npstat::AbsDistribution1D::operator!= ( const AbsDistribution1D &  r ) const

inline

Logical negation of operator==

operator==()

bool npstat::AbsDistribution1D::operator== ( const AbsDistribution1D &  r ) const

inline

Derived classes should not implement "operator==", implement "isEqual" instead

quantile()

virtual double npstat::AbsDistribution1D::quantile ( double  x ) const

pure virtual

The quantile function (inverse cdf)

Implemented in npstat::VerticallyInterpolatedDistribution1D, npstat::TruncatedDistribution1D, npstat::TransformedDistribution1D, npstat::RightCensoredDistribution, npstat::RatioOfNormals, npstat::LeftCensoredDistribution, npstat::InterpolatedDistribution1D, npstat::FoldedDistribution1D, npstat::ExpTiltedDistribution1D, npstat::EdgeworthSeries1D, npstat::DistributionMix1D, npstat::InterpolatedDistro1DNP, npstat::InterpolatedDistro1D1P, npstat::CompositeDistribution1D, npstat::ComparisonDistribution1D, npstat::AbsScalableDistribution1D, and npstat::ModulatedDistribution1D< Functor >.

random()

virtual unsigned npstat::AbsDistribution1D::random ( AbsRandomGenerator &  g, double *  generatedRandom  ) const

inlinevirtual

Random number generator according to the given distribution. Should return the number of random points used up from the generator.

Reimplemented in npstat::GaussianMixture1D, npstat::DistributionMix1D, npstat::RatioOfNormals, and npstat::AbsScalableDistribution1D.

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

• stat/AbsDistribution1D.hh