com.opengamma.strata.math.impl.statistics.distribution.GeneralizedExtremeValueDistribution Maven / Gradle / Ivy
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/*
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.strata.math.impl.statistics.distribution;
import com.google.common.math.DoubleMath;
import com.opengamma.strata.collect.ArgChecker;
/**
*
* 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:
* $$
* \begin{align*}
* f(x)&=\frac{t(x)^{\xi + 1}e^{-t(x)}}{\sigma}\quad\\
* t(x)&=
* \begin{cases}
* \left(1 + \xi\frac{x-\mu}{\sigma}\right)^{-\frac{1}{\xi}} & \text{if } \xi \neq 0,\\
* e^{-\frac{x-\mu}{\sigma}} & \text{if } \xi = 0.
* \end{cases}
* \end{align*}
* $$
*
*/
public class GeneralizedExtremeValueDistribution implements ProbabilityDistribution {
private final double _mu;
private final double _sigma;
private final double _ksi;
private final boolean _ksiIsZero;
/**
* Creates an instance.
*
* @param mu The location parameter
* @param sigma The scale parameter, not negative or zero
* @param ksi The shape parameter
*/
public GeneralizedExtremeValueDistribution(double mu, double sigma, double ksi) {
ArgChecker.isTrue(sigma >= 0, "sigma must be >= 0");
_mu = mu;
_sigma = sigma;
_ksi = ksi;
_ksiIsZero = DoubleMath.fuzzyEquals(ksi, 0d, 1e-13);
}
/**
* {@inheritDoc}
* @throws IllegalArgumentException If $x \not\in$ support
*/
@Override
public double getCDF(Double x) {
ArgChecker.notNull(x, "x");
return Math.exp(-getT(x));
}
/**
* {@inheritDoc}
* @return Not supported
* @throws UnsupportedOperationException always
*/
@Override
public double getInverseCDF(Double p) {
throw new UnsupportedOperationException();
}
/**
* {@inheritDoc}
* @throws IllegalArgumentException If $x \not\in$ support
*/
@Override
public double getPDF(Double x) {
ArgChecker.notNull(x, "x");
double t = getT(x);
return Math.pow(t, _ksi + 1) * Math.exp(-t) / _sigma;
}
/**
* {@inheritDoc}
* @return Not supported
* @throws UnsupportedOperationException always
*/
@Override
public double nextRandom() {
throw new UnsupportedOperationException();
}
/**
* Gets the location parameter.
*
* @return The location parameter
*/
public double getMu() {
return _mu;
}
/**
* Gets the scale parameter.
*
* @return The scale parameter
*/
public double getSigma() {
return _sigma;
}
/**
* Gets the shape parameter.
*
* @return The shape parameter
*/
public double getKsi() {
return _ksi;
}
private double getT(double x) {
if (_ksiIsZero) {
return Math.exp(-(x - _mu) / _sigma);
}
if (_ksi < 0 && x > _mu - _sigma / _ksi) {
throw new IllegalArgumentException("Support for GEV is in the range -infinity -> mu - sigma / ksi when ksi < 0");
}
if (_ksi > 0 && x < _mu - _sigma / _ksi) {
throw new IllegalArgumentException("Support for GEV is in the range mu - sigma / ksi -> +infinity when ksi > 0");
}
return Math.pow(1 + _ksi * (x - _mu) / _sigma, -1. / _ksi);
}
@Override
public int hashCode() {
int prime = 31;
int result = 1;
long temp;
temp = Double.doubleToLongBits(_ksi);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(_mu);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(_sigma);
result = prime * result + (int) (temp ^ (temp >>> 32));
return result;
}
@Override
public boolean equals(Object obj) {
if (this == obj) {
return true;
}
if (obj == null) {
return false;
}
if (getClass() != obj.getClass()) {
return false;
}
GeneralizedExtremeValueDistribution other = (GeneralizedExtremeValueDistribution) obj;
if (Double.doubleToLongBits(_ksi) != Double.doubleToLongBits(other._ksi)) {
return false;
}
if (Double.doubleToLongBits(_mu) != Double.doubleToLongBits(other._mu)) {
return false;
}
return Double.doubleToLongBits(_sigma) == Double.doubleToLongBits(other._sigma);
}
}