Package com.opengamma.strata.math.impl.statistics.distribution

Class GeneralizedExtremeValueDistribution

  • All Implemented Interfaces:
    ProbabilityDistribution<Double>
    public class GeneralizedExtremeValueDistribution
extends Object
implements ProbabilityDistribution<Double>
    The generalized extreme value distribution is a family of continuous probability distributions that combines the Gumbel (type I), Fréchet (type II) and Weibull (type III) families of distributions.

    This distribution has location parameter $\mu$, shape parameter $\xi$ and scale parameter $\sigma$, with $$ \begin{align*} \mu&\in\Re,\\ \xi&\in\Re,\\ \sigma&>0 \end{align*} $$ and support $$ \begin{align*} x\in \begin{cases} \left[\mu - \frac{\sigma}{\xi}, +\infty\right) & \text{when } \xi > 0\\ (-\infty,+\infty) & \text{when } \xi = 0\\\\ \left(-\infty, \mu - \frac{\sigma}{\xi}\right] & \text{when } \xi < 0 \end{cases} \end{align*} $$ The cdf is given by: $$ \begin{align*} F(x) &=e^{-t(x)}\\ t(x)&= \begin{cases} \left(1 + \xi\frac{x-\mu}{\sigma}\right)^{-\frac{1}{\xi}} & \text{if } \xi \neq 0,\\ e^{-\frac{x-\mu}{\sigma}} & \text{if } \xi = 0. \end{cases} \end{align*} $$ and the pdf by: $$ \begin{align*} f(x)&=\frac{t(x)^{\xi + 1}e^{-t(x)}}{\sigma}\quad\\ t(x)&= \begin{cases} \left(1 + \xi\frac{x-\mu}{\sigma}\right)^{-\frac{1}{\xi}} & \text{if } \xi \neq 0,\\ e^{-\frac{x-\mu}{\sigma}} & \text{if } \xi = 0. \end{cases} \end{align*} $$

    • Constructor Detail

      • GeneralizedExtremeValueDistribution

        public GeneralizedExtremeValueDistribution​(double mu,
                                           double sigma,
                                           double ksi)
        Creates an instance.
        Parameters:
        mu - The location parameter
        sigma - The scale parameter, not negative or zero
        ksi - The shape parameter