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package de.lmu.ifi.dbs.elki.math.statistics.distribution;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import java.util.Random;
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.math.random.RandomFactory;
import de.lmu.ifi.dbs.elki.utilities.Alias;
import de.lmu.ifi.dbs.elki.utilities.exceptions.ExceptionMessages;
import de.lmu.ifi.dbs.elki.utilities.exceptions.NotImplementedException;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;
/**
* Inverse Gaussian distribution aka Wald distribution
*
* @author Erich Schubert
* @since 0.6.0
*/
@Alias({ "InverseGaussianDistribution", "invgauss" })
public class WaldDistribution extends AbstractDistribution {
/**
* Location value
*/
private double mean;
/**
* Shape parameter
*/
private double shape;
/**
* Constructor for wald distribution
*
* @param mean Mean
* @param shape Shape parameter
* @param random Random generator
*/
public WaldDistribution(double mean, double shape, Random random) {
super(random);
this.mean = mean;
this.shape = shape;
}
/**
* Constructor for wald distribution
*
* @param mean Mean
* @param shape Shape parameter
* @param random Random generator
*/
public WaldDistribution(double mean, double shape, RandomFactory random) {
super(random);
this.mean = mean;
this.shape = shape;
}
/**
* Constructor for Gaussian distribution
*
* @param mean Mean
* @param shape Shape parameter
*/
public WaldDistribution(double mean, double shape) {
this(mean, shape, (Random) null);
}
@Override
public double pdf(double val) {
return pdf(val, mean, shape);
}
@Override
public double cdf(double val) {
return cdf(val, mean, shape);
}
/**
* @deprecated NOT YET IMPLEMENTED.
*/
@Override
@Deprecated
public double quantile(double q) {
return quantile(q, mean, shape);
}
@Override
public double nextRandom() {
double v = random.nextGaussian();
v *= v;
double x = mean + mean * .5 / shape * (mean * v - Math.sqrt(4. * mean * shape * v + mean * mean * v * v));
double u = random.nextDouble();
if (u * (mean + x) <= mean) {
return x;
} else {
return mean * mean / x;
}
}
@Override
public String toString() {
return "WaldDistribution(mean=" + mean + ", shape=" + shape + ")";
}
/**
* Probability density function of the Wald distribution.
*
*
* @param x The value.
* @param mu The mean.
* @param shape Shape parameter
* @return PDF of the given Wald distribution at x.
*/
public static double pdf(double x, double mu, double shape) {
if (!(x > 0)) {
return 0;
}
final double v = (x - mu);
return Math.sqrt(shape / (MathUtil.TWOPI * x * x * x)) * Math.exp(-shape * v * v / (2. * mu * mu * x));
}
/**
* Cumulative probability density function (CDF) of a Wald distribution.
*
* @param x value to evaluate CDF at
* @param mu Mean value
* @param shape Shape parameter
* @return The CDF of the given Wald distribution at x.
*/
public static double cdf(double x, double mu, double shape) {
if (!(x > 0.)) {
return 0.;
}
// TODO: accelerate by caching exp(2 * shape / mu).
final double v0 = x / mu;
final double v1 = Math.sqrt(shape / x);
double c1 = NormalDistribution.standardNormalCDF(v1 * (v0 - 1.));
double c2 = NormalDistribution.standardNormalCDF(-v1 * (v0 + 1.));
if (c2 > 0.) {
return c1 + Math.exp(2 * shape / mu) * c2;
} else {
return c1;
}
}
/**
* Inverse cumulative probability density function (probit) of a Wald
* distribution.
*
* @param x value to evaluate probit function at
* @param mu Mean value
* @param shape Shape parameter
* @return The probit of the given Wald distribution at x.
*
* @deprecated NOT YET IMPLEMENTED.
*/
@Deprecated
public static double quantile(double x, double mu, double shape) {
// FIXME: implement!
throw new NotImplementedException(ExceptionMessages.UNSUPPORTED_NOT_YET);
}
/**
* Parameterization class
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractDistribution.Parameterizer {
/** Parameters. */
double mean, shape;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
DoubleParameter meanP = new DoubleParameter(LOCATION_ID);
if (config.grab(meanP)) {
mean = meanP.doubleValue();
}
DoubleParameter shapeP = new DoubleParameter(SHAPE_ID);
if (config.grab(shapeP)) {
shape = shapeP.doubleValue();
}
}
@Override
protected WaldDistribution makeInstance() {
return new WaldDistribution(mean, shape, rnd);
}
}
}
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