de.lmu.ifi.dbs.elki.math.statistics.distribution

Class GeneralizedParetoDistribution

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedParetoDistribution

All Implemented Interfaces:

Distribution

public class GeneralizedParetoDistribution
extends AbstractDistribution

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 and Description
static class	GeneralizedParetoDistribution.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and 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)

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

random

Constructor Summary

Constructors

Constructor and Description
GeneralizedParetoDistribution(double mu, double sigma, double xi) Constructor.
GeneralizedParetoDistribution(double mu, double sigma, double xi, java.util.Random random) Constructor.
GeneralizedParetoDistribution(double mu, double sigma, double xi, RandomFactory random) Constructor.

Method Summary

Modifier and Type	Method and 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 de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

nextRandom

Methods inherited from class java.lang.Object

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

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)

GeneralizedParetoDistribution

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

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

random - Random number generator

GeneralizedParetoDistribution

public GeneralizedParetoDistribution(double mu,
                                     double sigma,
                                     double xi,
                                     java.util.Random random)

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

xi - Shape parameter xi (= -kappa)

random - Random number generator

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

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

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.

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.

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