Package elki.math.statistics.distribution

Class GeneralizedParetoDistribution

java.lang.Object

elki.math.statistics.distribution.GeneralizedParetoDistribution

All Implemented Interfaces:

Distribution

public class GeneralizedParetoDistribution
extends java.lang.Object
implements Distribution

Generalized Pareto Distribution (GPD), popular for modeling long tail distributions.

Since:

0.7.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	GeneralizedParetoDistribution.Par	Parameterization class

Nested classes/interfaces inherited from interface elki.math.statistics.distribution.Distribution

Distribution.Parameterizer

Field Summary

Fields

Modifier and Type	Field	Description
(package private) double	mu	Parameters (location, scale, shape)
(package private) double	sigma	Parameters (location, scale, shape)
(package private) double	xi	Parameters (location, scale, shape)

Constructor Summary

Constructors

Constructor	Description
GeneralizedParetoDistribution(double mu, double sigma, double xi)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	cdf(double val)	Return the cumulative density function at the given value.
static double	cdf(double val, double mu, double sigma, double xi)	CDF of GPD distribution
double	getMu()	Location parameter
double	getSigma()	Scale parameter
double	getXi()	Shape parameter
double	logpdf(double x)	Return the log density of an existing value
static double	logpdf(double x, double mu, double sigma, double xi)	PDF of GPD distribution
double	pdf(double x)	Return the density of an existing value
static double	pdf(double x, double mu, double sigma, double xi)	PDF of GPD distribution
double	quantile(double val)	Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double val, double mu, double sigma, double xi)	Quantile function of GPD distribution
java.lang.String	toString()	Describe the distribution

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface elki.math.statistics.distribution.Distribution

nextRandom

Field Detail

mu

final double mu

Parameters (location, scale, shape)

sigma

final double sigma

Parameters (location, scale, shape)

xi

final double xi

Parameters (location, scale, shape)

Constructor Detail

GeneralizedParetoDistribution

public GeneralizedParetoDistribution(double mu,
                                     double sigma,
                                     double xi)

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

Method Detail

getMu

public double getMu()

Location parameter

Returns:

Location

getSigma

public double getSigma()

Scale parameter

Returns:

Sigma

getXi

public double getXi()

Shape parameter

Returns:

xi

pdf

public static double pdf(double x,
                         double mu,
                         double sigma,
                         double xi)

PDF of GPD distribution

Parameters:

x - Value

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

Returns:

PDF at position x.

pdf

public double pdf(double x)

Description copied from interface: Distribution

Return the density of an existing value

Specified by:

pdf in interface Distribution

Parameters:

x - existing value

Returns:

distribution density

logpdf

public static double logpdf(double x,
                            double mu,
                            double sigma,
                            double xi)

PDF of GPD distribution

Parameters:

x - Value

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

Returns:

PDF at position x.

logpdf

public double logpdf(double x)

Description copied from interface: Distribution

Return the log density of an existing value

Specified by:

logpdf in interface Distribution

Parameters:

x - existing value

Returns:

log distribution density

cdf

public static double cdf(double val,
                         double mu,
                         double sigma,
                         double xi)

CDF of GPD distribution

Parameters:

val - Value

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

Returns:

CDF at position x.

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Specified by:

cdf in interface Distribution

Parameters:

val - existing value

Returns:

cumulative density

quantile

public static double quantile(double val,
                              double mu,
                              double sigma,
                              double xi)

Quantile function of GPD distribution

Parameters:

val - Value

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

Returns:

Quantile function at position x.

quantile

public double quantile(double val)

Description copied from interface: Distribution

Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.

Specified by:

quantile in interface Distribution

Parameters:

val - Quantile to find

Returns:

Quantile position

toString

public java.lang.String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class java.lang.Object

Returns:

description