npstat::EdgeworthSeries1D Class Reference

Inheritance diagram for npstat::EdgeworthSeries1D:

Public Member Functions
	EdgeworthSeries1D (const std::vector< double > &cumulants, EdgeworthSeriesMethod m, unsigned order, bool slrMode=false)
virtual EdgeworthSeries1D *	clone () const
virtual double	density (double x) const
virtual double	cdf (double x) const
virtual double	exceedance (double x) const
virtual double	quantile (double x) const
double	inverseExceedance (double x) const
EdgeworthSeriesMethod	method () const
bool	slrMode () const
unsigned	order () const
double	cum (const unsigned k) const
double	edgMean () const
double	edgStdev () const
double	densityFactor (double x) const
double	cdfFactor (double x) const
double	empiricalCentralMoment (unsigned degree) const
virtual gs::ClassId	classId () const
virtual bool	write (std::ostream &) const
Public Member Functions inherited from npstat::AbsDistribution1D
bool	operator== (const AbsDistribution1D &r) const
bool	operator!= (const AbsDistribution1D &r) const
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

Static Public Member Functions
static const char *	classname ()
static unsigned	version ()
static EdgeworthSeries1D *	read (const gs::ClassId &id, std::istream &is)
Static Public Member Functions inherited from npstat::AbsDistribution1D
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

Constructor & Destructor Documentation

EdgeworthSeries1D()

npstat::EdgeworthSeries1D::EdgeworthSeries1D	(	const std::vector< double > &	cumulants,
		EdgeworthSeriesMethod	m,
		unsigned	order,
		bool	slrMode = false
	)

Constructor arguments are as follows:

cumulants – The vector of cumulants. The first element of the vector (with index 0) is the first cumulant, the second element is the second, etc.

m – The method used to construct the distribition. See header EdgeworthSeriesMethod.hh for further explanations.

order – The expansion order in powers of 1/sqrt(n). O(1/sqrt(n)) is the 0th order, O(1/n) is the first order, O(1/(n sqrt(n)) is the second order, etc. Currently, the highest supported order is 14 for EDGEWORTH_CLASSICAL method in a non-SLR mode, and 4 in all other situations.

slrMode – If true, we will assume that the kth cumulant vanishes (for k > 2) to O(n^{-k/2}) instead of the usual O(n^{-(k-2)/2}). This is the case for the SLR statistic.

Member Function Documentation

cdf()

virtual double npstat::EdgeworthSeries1D::cdf ( double  x ) const

virtual

Cumulative distribution function

Implements npstat::AbsDistribution1D.

cdfFactor()

double npstat::EdgeworthSeries1D::cdfFactor

(

double

x

)

const

Edgeworth expansion factor for the CDF

classId()

virtual gs::ClassId npstat::EdgeworthSeries1D::classId ( ) const

inlinevirtual

Prototype needed for I/O

Implements npstat::AbsDistribution1D.

clone()

virtual EdgeworthSeries1D* npstat::EdgeworthSeries1D::clone ( ) const

inlinevirtual

"Virtual copy constructor"

Implements npstat::AbsDistribution1D.

cum()

double npstat::EdgeworthSeries1D::cum ( const unsigned  k ) const

inline

This function returns the constructor argument, not the real cumulant which depends on the expansion order used. Use the "empiricalCentralMoment" function and then convert central moments to cumulants if you need real cumulants. The real mean is 0 if order == 0 and cum(0) if order > 0.

density()

virtual double npstat::EdgeworthSeries1D::density ( double  x ) const

virtual

Probability density

Implements npstat::AbsDistribution1D.

densityFactor()

double npstat::EdgeworthSeries1D::densityFactor

(

double

x

)

const

Edgeworth expansion factor for the density

edgMean()

double npstat::EdgeworthSeries1D::edgMean

(

)

const

Mean of the function used to build the expansion

edgStdev()

double npstat::EdgeworthSeries1D::edgStdev

(

)

const

Standard deviation of the function used to build the expansion

empiricalCentralMoment()

double npstat::EdgeworthSeries1D::empiricalCentralMoment

(

unsigned

degree

)

const

Actual central moment of the density (evaluated numerically for degree > 1 using Gauss-Hermite quadrature)

exceedance()

virtual double npstat::EdgeworthSeries1D::exceedance ( double  x ) const

virtual

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

Implements npstat::AbsDistribution1D.

inverseExceedance()

double npstat::EdgeworthSeries1D::inverseExceedance

(

double

x

)

const

Inverse exceedance function. More precise than "quantile(1 - x)" for small x.

isEqual()

virtual bool npstat::EdgeworthSeries1D::isEqual ( const AbsDistribution1D &  ) const

protectedvirtual

Comparison for equality. To be implemented by derived classes.

Implements npstat::AbsDistribution1D.

method()

EdgeworthSeriesMethod npstat::EdgeworthSeries1D::method ( ) const

inline

Inspector

quantile()

virtual double npstat::EdgeworthSeries1D::quantile ( double  x ) const

virtual

The quantile function (inverse cdf)

Implements npstat::AbsDistribution1D.

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

• stat/EdgeworthSeries1D.hh