/**
* 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.StudentT;
import cern.jet.random.engine.MersenneTwister64;
import cern.jet.random.engine.RandomEngine;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.function.special.InverseIncompleteBetaFunction;
/**
* Student's T-distribution is a continuous probability distribution with probability density function
* $$
* \begin{align*}
* f(x) = \frac{\Gamma\left(\frac{\nu + 1}{2}\right)}{\sqrt{\nu\pi}\Gamma(\left(\frac{\nu}{2}\right)}\left(1 + \frac{x^2}{\nu}\right)^{-\frac{1}{2}(\nu + 1)}
* \end{align*}
* $$
* where $\nu$ is the number of degrees of freedom and $\Gamma$ is the Gamma function ({@link com.opengamma.analytics.math.function.special.GammaFunction}).
* <p>
* This class is a wrapper for the <a href="http://acs.lbl.gov/software/colt/api/cern/jet/random/StudentT.html">Colt</a> implementation of Student's T-distribution for cdf and pdf calculations
* and Student's T-distributed random number generation.
*/
public class StudentTDistribution implements ProbabilityDistribution<Double> {
// TODO need a better seed
private final double _degFreedom;
private final StudentT _dist;
private final Function1D<Double, Double> _beta;
/**
* @param degFreedom The number of degrees of freedom, not negative or zero
*/
public StudentTDistribution(final double degFreedom) {
this(degFreedom, new MersenneTwister64(new Date()));
}
/**
* @param degFreedom The number of degrees of freedom, not negative or zero
* @param engine A generator of uniform random numbers, not null
*/
public StudentTDistribution(final double degFreedom, final RandomEngine engine) {
Validate.isTrue(degFreedom > 0, "degrees of freedom");
Validate.notNull(engine);
_degFreedom = degFreedom;
_dist = new StudentT(degFreedom, engine);
_beta = new InverseIncompleteBetaFunction(degFreedom / 2., 0.5);
}
/**
* {@inheritDoc}
*/
@Override
public double getCDF(final Double x) {
Validate.notNull(x);
return _dist.cdf(x);
}
/**
* {@inheritDoc}
*/
@Override
public double getPDF(final Double x) {
Validate.notNull(x);
return _dist.pdf(x);
}
/**
* {@inheritDoc}
*/
@Override
public double nextRandom() {
return _dist.nextDouble();
}
/**
* {@inheritDoc}
* The inverse cdf is given by:
* $$
* \begin{align*}
* F(P) &= \mathrm{sign}(p - \frac{1}{2})\sqrt{\frac{\nu}{x - 1}}\\
* x &= B(2 \min(p, 1-p))
* \end{align*}
* $$
* where $B$ is the inverse incomplete Beta function ({@link com.opengamma.analytics.math.function.special.InverseIncompleteBetaFunction}).
*/
@Override
public double getInverseCDF(final Double p) {
Validate.notNull(p);
Validate.isTrue(p >= 0 && p <= 1, "Probability must be >= 0 and <= 1");
final double x = _beta.evaluate(2 * Math.min(p, 1 - p));
return Math.signum(p - 0.5) * Math.sqrt(_degFreedom * (1. / x - 1));
}
/**
* @return The number of degrees of freedom
*/
public double getDegreesOfFreedom() {
return _degFreedom;
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
long temp;
temp = Double.doubleToLongBits(_degFreedom);
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 StudentTDistribution other = (StudentTDistribution) obj;
return Double.doubleToLongBits(_degFreedom) == Double.doubleToLongBits(other._degFreedom);
}
}