com.opengamma.analytics.math.statistics.distribution.GeneralizedParetoDistribution.java Source code

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Here is the source code for com.opengamma.analytics.math.statistics.distribution.GeneralizedParetoDistribution.java

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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.analytics.math.statistics.distribution;

import java.util.Date;

import org.apache.commons.lang.NotImplementedException;
import org.apache.commons.lang.Validate;

import cern.jet.random.engine.MersenneTwister64;
import cern.jet.random.engine.RandomEngine;

import com.opengamma.util.CompareUtils;

/**
 * 
 * The generalized Pareto distribution is a family of power law probability
 * distributions with location parameter $\mu$, shape parameter $\xi$ and scale
 * parameter $\sigma$, where
 * $$
 * \begin{eqnarray*}
 * \mu&\in&\Re,\\
 * \xi&\in&\Re,\\
 * \sigma&>&0
 * \end{eqnarray*}
 * $$
 * and with support
 * $$
 * \begin{eqnarray*}
 * x\geq\mu\quad\quad\quad(\xi\geq 0)\\
 * \mu\leq x\leq\mu-\frac{\sigma}{\xi}\quad(\xi<0)
 * \end{eqnarray*}
 * $$
 * The cdf is given by:
 * $$
 * \begin{align*}
 * F(z)&=1-\left(1 + \xi z\right)^{-\frac{1}{\xi}}\\
 * z&=\frac{x-\mu}{\sigma}
 * \end{align*}
 * $$
 * and the pdf is given by:
 * $$
 * \begin{align*}
 * f(z)&=\frac{\left(1+\xi z\right)^{-\left(\frac{1}{\xi} + 1\right)}}{\sigma}\\
 * z&=\frac{x-\mu}{\sigma}
 * \end{align*}
 * $$
 * Given a uniform random number variable $U$ drawn from the interval $(0,1]$, a
 * Pareto-distributed random variable with parameters $\mu$, $\sigma$ and
 * $\xi$ is given by
 * $$
 * \begin{align*}
 * X=\mu + \frac{\sigma\left(U^{-\xi}-1\right)}{\xi}\sim GPD(\mu,\sigma,\xi)
 * \end{align*}
 * $$
 */
public class GeneralizedParetoDistribution implements ProbabilityDistribution<Double> {
    // TODO check cdf, pdf for support
    private final double _mu;
    private final double _sigma;
    private final double _ksi;
    // TODO better seed
    private final RandomEngine _engine;

    /**
     * 
     * @param mu The location parameter
     * @param sigma The scale parameter, not negative or zero
     * @param ksi The shape parameter, not zero
     */
    public GeneralizedParetoDistribution(final double mu, final double sigma, final double ksi) {
        this(mu, sigma, ksi, new MersenneTwister64(new Date()));
    }

    /**
     * 
     * @param mu The location parameter
     * @param sigma The scale parameter
     * @param ksi The shape parameter
     * @param engine A uniform random number generator, not null
     */
    public GeneralizedParetoDistribution(final double mu, final double sigma, final double ksi,
            final RandomEngine engine) {
        Validate.isTrue(sigma > 0, "sigma must be > 0");
        Validate.isTrue(!CompareUtils.closeEquals(ksi, 0, 1e-15), "ksi cannot be zero");
        Validate.notNull(engine);
        _mu = mu;
        _sigma = sigma;
        _ksi = ksi;
        _engine = engine;
    }

    /**
     * @return The location parameter
     */
    public double getMu() {
        return _mu;
    }

    /**
     * @return The scale parameter
     */
    public double getSigma() {
        return _sigma;
    }

    /**
     * @return The shape parameter
     */
    public double getKsi() {
        return _ksi;
    }

    /**
     * {@inheritDoc}
     * @throws IllegalArgumentException If $x \not\in$ support
     */
    @Override
    public double getCDF(final Double x) {
        Validate.notNull(x);
        return 1 - Math.pow(1 + _ksi * getZ(x), -1. / _ksi);
    }

    /**
     * {@inheritDoc}
     * @return Not supported
     * @throws NotImplementedException
     */
    @Override
    public double getInverseCDF(final Double p) {
        throw new NotImplementedException();
    }

    /**
    * {@inheritDoc} 
    * @throws IllegalArgumentException If $x \not\in$ support
    */
    @Override
    public double getPDF(final Double x) {
        Validate.notNull(x);
        return Math.pow(1 + _ksi * getZ(x), -(1. / _ksi + 1)) / _sigma;
    }

    /**
     * {@inheritDoc} 
     */
    @Override
    public double nextRandom() {
        return _mu + _sigma * (Math.pow(_engine.nextDouble(), -_ksi) - 1) / _ksi;
    }

    private double getZ(final double x) {
        if (_ksi > 0 && x < _mu) {
            throw new IllegalArgumentException("Support for GPD is in the range x >= mu if ksi > 0");
        }
        if (_ksi < 0 && (x <= _mu || x >= _mu - _sigma / _ksi)) {
            throw new IllegalArgumentException(
                    "Support for GPD is in the range mu <= x <= mu - sigma / ksi if ksi < 0");
        }
        return (x - _mu) / _sigma;
    }

    @Override
    public int hashCode() {
        final 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(final Object obj) {
        if (this == obj) {
            return true;
        }
        if (obj == null) {
            return false;
        }
        if (getClass() != obj.getClass()) {
            return false;
        }
        final GeneralizedParetoDistribution other = (GeneralizedParetoDistribution) 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);
    }

}