Package elki.math.statistics.distribution

Class GeneralizedExtremeValueDistribution

java.lang.Object

elki.math.statistics.distribution.GeneralizedExtremeValueDistribution

All Implemented Interfaces:

Distribution

public class GeneralizedExtremeValueDistribution
extends java.lang.Object
implements Distribution

Generalized Extreme Value (GEV) distribution, also known as Fisher–Tippett distribution.

This is a generalization of the Frechnet, Gumbel and (reversed) Weibull distributions.

Implementation notice: In ELKI 0.8.0, the sign of the shape was negated.

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	GeneralizedExtremeValueDistribution.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	k	Parameters (location, scale, shape)
(package private) double	mu	Parameters (location, scale, shape)
(package private) double	sigma	Parameters (location, scale, shape)

Constructor Summary

Constructors

Constructor	Description
GeneralizedExtremeValueDistribution(double mu, double sigma, double k)	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 k)	CDF of GEV distribution
double	getK()	Get the k parameter.
double	getMu()	Get location.
double	getSigma()	Get sigma.
double	logpdf(double x)	Return the log density of an existing value
static double	logpdf(double x, double mu, double sigma, double k)	log PDF of GEV distribution
double	pdf(double x)	Return the density of an existing value
static double	pdf(double x, double mu, double sigma, double k)	PDF of GEV 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 k)	Quantile function of GEV 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)

k

final double k

Parameters (location, scale, shape)

Constructor Detail

GeneralizedExtremeValueDistribution

public GeneralizedExtremeValueDistribution(double mu,
                                           double sigma,
                                           double k)

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

Method Detail

getMu

public double getMu()

Get location.

Returns:

Location

getSigma

public double getSigma()

Get sigma.

Returns:

Sigma

getK

public double getK()

Get the k parameter.

Returns:

k

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

pdf

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

PDF of GEV distribution

Parameters:

x - Value

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

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

logpdf

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

log PDF of GEV distribution

Parameters:

x - Value

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

Returns:

PDF 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

cdf

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

CDF of GEV distribution

Parameters:

val - Value

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

Returns:

CDF 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

quantile

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

Quantile function of GEV distribution

Parameters:

val - Value

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

Returns:

Quantile function at position x.

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