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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.random.RandomFactory;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;
/**
* Weibull distribution.
*
* @author Erich Schubert
* @since 0.6.0
*/
public class WeibullDistribution extends AbstractDistribution {
/**
* Shift offset.
*/
double theta = 0.;
/**
* Shape parameter k.
*/
double k;
/**
* Lambda parameter.
*/
double lambda;
/**
* Constructor.
*
* @param k Shape parameter
* @param lambda Scale parameter
*/
public WeibullDistribution(double k, double lambda) {
this(k, lambda, 0.0, (Random) null);
}
/**
* Constructor.
*
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
*/
public WeibullDistribution(double k, double lambda, double theta) {
this(k, lambda, theta, (Random) null);
}
/**
* Constructor.
*
* @param k Shape parameter
* @param lambda Scale parameter
* @param random Random number generator
*/
public WeibullDistribution(double k, double lambda, Random random) {
this(k, lambda, 0., random);
}
/**
* Constructor.
*
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
* @param random Random number generator
*/
public WeibullDistribution(double k, double lambda, double theta, Random random) {
super(random);
this.k = k;
this.lambda = lambda;
this.theta = theta;
}
/**
* Constructor.
*
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
* @param random Random number generator
*/
public WeibullDistribution(double k, double lambda, double theta, RandomFactory random) {
super(random);
this.k = k;
this.lambda = lambda;
this.theta = theta;
}
@Override
public double pdf(double x) {
return pdf(x, k, lambda, theta);
}
/**
* PDF of Weibull distribution
*
* @param x Value
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
* @return PDF at position x.
*/
public static double pdf(double x, double k, double lambda, double theta) {
if (x > theta) {
double xl = (x - theta) / lambda;
return k / lambda * Math.pow(xl, k - 1) * Math.exp(-Math.pow(xl, k));
} else {
return 0.;
}
}
/**
* CDF of Weibull distribution
*
* @param val Value
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
* @return CDF at position x.
*/
public static double cdf(double val, double k, double lambda, double theta) {
if (val > theta) {
return 1.0 - Math.exp(-Math.pow((val - theta) / lambda, k));
} else {
return 0.0;
}
}
@Override
public double cdf(double val) {
return cdf(val, k, lambda, theta);
}
/**
* Quantile function of Weibull distribution
*
* @param val Value
* @param k Shape parameter
* @param lambda Scale parameter
* @param theta Shift offset parameter
* @return Quantile function at position x.
*/
public static double quantile(double val, double k, double lambda, double theta) {
if (val < 0.0 || val > 1.0) {
return Double.NaN;
} else if (val == 0) {
return 0.0;
} else if (val == 1) {
return Double.POSITIVE_INFINITY;
} else {
return theta + lambda * Math.pow(-Math.log(1.0 - val), 1.0 / k);
}
}
@Override
public double quantile(double val) {
return quantile(val, k, lambda, theta);
}
@Override
public double nextRandom() {
return theta + lambda * Math.pow(-Math.log(1 - random.nextDouble()), 1. / k);
}
@Override
public String toString() {
return "WeibullDistribution(k=" + k + ", lambda=" + lambda + ", theta=" + theta + ")";
}
/**
* Parameterization class
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractDistribution.Parameterizer {
/** Parameters. */
double theta, k, lambda;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
DoubleParameter thetaP = new DoubleParameter(LOCATION_ID, 0.);
if (config.grab(thetaP)) {
theta = thetaP.doubleValue();
}
DoubleParameter lambdaP = new DoubleParameter(SCALE_ID);
if (config.grab(lambdaP)) {
lambda = lambdaP.doubleValue();
}
DoubleParameter kP = new DoubleParameter(SHAPE_ID);
if (config.grab(kP)) {
k = kP.doubleValue();
}
}
@Override
protected WeibullDistribution makeInstance() {
return new WeibullDistribution(theta, k, lambda, rnd);
}
}
}
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