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

Class FrechetDistribution

java.lang.Object

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

dev.nm.stat.evt.evd.univariate.FrechetDistribution

All Implemented Interfaces:

ProbabilityDistribution, UnivariateEVD

public class FrechetDistribution
extends GeneralizedEVD

The Fréchet distribution is a special case (Type II) of the generalized extreme value distribution, with \(\xi>0\). The cumulative distribution function is \[ F(x;\mu,\sigma,\xi)= \begin{cases} 0 & x\leq \mu \\ e^{-((x-\mu)/\sigma)^{-\alpha}} & x>\mu. \end{cases} \]

The R equivalent functions are evd::dfrechet, evd::pfrechet, evd::qfrechet, evd::rfrechet.

See Also:

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

Constructor Summary

Constructors

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

FrechetDistribution

public FrechetDistribution()

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

FrechetDistribution

public FrechetDistribution(double location,
 double scale,
 double shape)

Create an instance with the given parameter values.

Parameters:

location - the location parameter \(\mu\)

scale - the scale parameter \(\sigma\)

shape - the shape parameter \(\alpha\)