Package dev.nm.stat.evt.evd.univariate

Class GumbelDistribution

java.lang.Object

dev.nm.stat.evt.evd.univariate.GeneralizedEVD

dev.nm.stat.evt.evd.univariate.GumbelDistribution

All Implemented Interfaces:

ProbabilityDistribution, UnivariateEVD

public class GumbelDistribution
extends GeneralizedEVD

The Gumbel distribution is a special case (Type I) of the generalized extreme value distribution, with \(\xi=0\). The cumulative distribution function is \[ F(x;\mu,\sigma,0)=e^{-e^{-(x-\mu)/\sigma}} \;\; \text{for} \;\; x\in\mathbb R. \] The R equivalent functions are evd::dgumbel, evd::pgumbel, evd::qgumbel, evd::rgumbel.

See Also:

• Wikipedia: Gumbel distribution
• Wikipedia: Generalized extreme value distribution - Link to Fréchet, Weibull and Gumbel families

Constructor Summary

Constructors

Constructor	Description
GumbelDistribution()	Create an instance with the default parameter values: location \(\mu=0\), scale \(\sigma=1\).
GumbelDistribution(double location, double scale)	Create an instance with the given parameter values.

Method Summary

Methods inherited from class dev.nm.stat.evt.evd.univariate.GeneralizedEVD

cdf, density, entropy, getLocation, getScale, getShape, kurtosis, logDensity, marginalInverseTransform, marginalTransform, mean, median, moment, quantile, skew, variance

Methods inherited from class java.lang.Object

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

Constructor Details

GumbelDistribution

public GumbelDistribution()

Create an instance with the default parameter values: location \(\mu=0\), scale \(\sigma=1\).

GumbelDistribution

public GumbelDistribution(double location,
 double scale)

Create an instance with the given parameter values.

Parameters:

location - the location parameter \(\mu\)

scale - the scale parameter \(\sigma\)