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

Class GumbelDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

public class GumbelDistribution
extends AbstractDistribution

Gumbel distribution, also known as Log-Weibull distribution.

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
(package private) double	beta Shape parameter beta.
(package private) double	mu Mode parameter mu.

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

random

Constructor Summary

Constructors

Constructor and Description
GumbelDistribution(double mu, double beta) Constructor.
GumbelDistribution(double mu, double beta, Random random) Constructor.
GumbelDistribution(double mu, double beta, 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 beta) CDF of Weibull distribution
double	nextRandom() Generate a new random value
double	pdf(double x) Return the density of an existing value
static double	pdf(double x, double mu, double beta) PDF of Weibull 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 beta) Quantile function of Weibull distribution
String	toString() Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

mu

double mu

Mode parameter mu.

beta

double beta

Shape parameter beta.

Constructor Detail

GumbelDistribution

public GumbelDistribution(double mu,
                          double beta)

Constructor.

Parameters:

mu - Mode

beta - Shape

GumbelDistribution

public GumbelDistribution(double mu,
                          double beta,
                          Random random)

Constructor.

Parameters:

mu - Mode

beta - Shape

random - Random number generator

GumbelDistribution

public GumbelDistribution(double mu,
                          double beta,
                          RandomFactory random)

Constructor.

Parameters:

mu - Mode

beta - Shape

random - Random number generator

Method Detail

pdf

public static double pdf(double x,
                         double mu,
                         double beta)

PDF of Weibull distribution

Parameters:

x - Value

mu - Mode

beta - Shape

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 beta)

CDF of Weibull distribution

Parameters:

val - Value

mu - Mode

beta - Shape

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 beta)

Quantile function of Weibull distribution

Parameters:

val - Value

mu - Mode

beta - Shape

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

nextRandom

public double nextRandom()

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Overrides:

nextRandom in class AbstractDistribution

Returns:

new random value

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