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

Class GeneralizedExtremeValueDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

public class GeneralizedExtremeValueDistribution
extends AbstractDistribution

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: apparently (see unit tests), our definition differs from the scipy definition by having the negative shape.

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GeneralizedExtremeValueDistribution.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and 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)

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

random

Constructor Summary

Constructors

Constructor and Description
GeneralizedExtremeValueDistribution(double mu, double sigma, double k) Constructor.
GeneralizedExtremeValueDistribution(double mu, double sigma, double k, Random random) Constructor.
GeneralizedExtremeValueDistribution(double mu, double sigma, double k, RandomFactory random) Constructor.

Method Summary

Methods

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 k) CDF 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
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)

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

GeneralizedExtremeValueDistribution

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

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

random - Random number generator

GeneralizedExtremeValueDistribution

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

Constructor.

Parameters:

mu - Location parameter mu

sigma - Scale parameter sigma

k - Shape parameter k

random - Random number generator

Method Detail

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.

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

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.

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 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.

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 String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class Object

Returns:

description