/**
* 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.Validate;
import cern.jet.random.ChiSquare;
import cern.jet.random.engine.MersenneTwister64;
import cern.jet.random.engine.RandomEngine;
import com.opengamma.analytics.math.function.Function2D;
import com.opengamma.analytics.math.function.special.InverseIncompleteGammaFunction;
/**
* A $\chi^2$ distribution with $k$ degrees of freedom is the distribution of
* the sum of squares of $k$ independent standard normal random variables with
* cdf and inverse cdf
* $$
* \begin{align*}
* F(x) &=\frac{\gamma\left(\frac{k}{2}, \frac{x}{2}\right)}{\Gamma\left(\frac{k}{2}\right)}\\
* F^{-1}(p) &= 2\gamma^{-1}\left(\frac{k}{2}, p\right)
* \end{align*}
* $$
* where $\gamma(y, z)$ is the lower incomplete Gamma function and $\Gamma(y)$
* is the Gamma function. The pdf is given by:
* $$
* \begin{align*}
* f(x)=\frac{x^{\frac{k}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{k}{2}}\Gamma\left(\frac{k}{2}\right)}
* \end{align*}
* $$
* This implementation uses the CERN <a href="http://acs.lbl.gov/~hoschek/colt/api/index.html">colt</a> package for the
* cdf, pdf and $\chi^2$-distributed random numbers.
*
*/
public class ChiSquareDistribution implements ProbabilityDistribution<Double> {
private final Function2D<Double, Double> _inverseFunction = new InverseIncompleteGammaFunction();
private final ChiSquare _chiSquare;
private final double _degrees;
/**
* @param degrees The degrees of freedom of the distribution, not less than one
*/
public ChiSquareDistribution(final double degrees) {
this(degrees, new MersenneTwister64(new Date()));
}
/**
* @param degrees The degrees of freedom of the distribution, not less than one
* @param engine A uniform random number generator, not null
*/
public ChiSquareDistribution(final double degrees, final RandomEngine engine) {
Validate.isTrue(degrees >= 1, "Degrees of freedom must be greater than or equal to one");
Validate.notNull(engine);
_chiSquare = new ChiSquare(degrees, engine);
_degrees = degrees;
}
/**
* {@inheritDoc}
*/
@Override
public double getCDF(final Double x) {
Validate.notNull(x);
return _chiSquare.cdf(x);
}
/**
* {@inheritDoc}
*/
@Override
public double getPDF(final Double x) {
Validate.notNull(x);
return _chiSquare.pdf(x);
}
/**
* {@inheritDoc}
*/
@Override
public double getInverseCDF(final Double p) {
Validate.notNull(p);
Validate.isTrue(p >= 0 && p <= 1, "Probability must lie between 0 and 1");
return 2 * _inverseFunction.evaluate(0.5 * _degrees, p);
}
/**
* {@inheritDoc}
*/
@Override
public double nextRandom() {
return _chiSquare.nextDouble();
}
/**
* @return The number of degrees of freedom
*/
public double getDegreesOfFreedom() {
return _degrees;
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
long temp;
temp = Double.doubleToLongBits(_degrees);
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 ChiSquareDistribution other = (ChiSquareDistribution) obj;
return Double.doubleToLongBits(_degrees) == Double.doubleToLongBits(other._degrees);
}
}