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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) 2013
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.utilities.Alias;
/**
* Log-Normal distribution.
*
* The parameterization of this class is somewhere inbetween of GNU R and SciPy.
* Similar to GNU R we use the logmean and logstddev. Similar to Scipy, we also
* have a location parameter that shifts the distribution.
*
* Our implementation maps to SciPy's as follows:
* <tt>scipy.stats.lognorm(logstddev, shift, math.exp(logmean))</tt>
*
* @author Erich Schubert
*/
@Alias({ "lognormal" })
public class LogNormalDistribution implements Distribution {
/**
* Mean value for the generator
*/
private double logmean;
/**
* Standard deviation
*/
private double logstddev;
/**
* Additional shift factor
*/
private double shift = 0.;
/**
* The random generator.
*/
private Random random;
/**
* Constructor for Log-Normal distribution
*
* @param logmean Mean
* @param logstddev Standard Deviation
* @param shift Shifting offset
* @param random Random generator
*/
public LogNormalDistribution(double logmean, double logstddev, double shift, Random random) {
super();
this.logmean = logmean;
this.logstddev = logstddev;
this.shift = shift;
this.random = random;
}
/**
* Constructor.
*
* @param logmean Mean
* @param logstddev Standard deviation
* @param shift Shifting offset
*/
public LogNormalDistribution(double logmean, double logstddev, double shift) {
this(logmean, logstddev, shift, null);
}
@Override
public double pdf(double val) {
return pdf(val - shift, logmean, logstddev);
}
@Override
public double cdf(double val) {
return cdf(val - shift, logmean, logstddev);
}
@Override
public double quantile(double val) {
return quantile(val, logmean, logstddev) + shift;
}
/**
* Probability density function of the normal distribution.
*
* <pre>
* 1/(SQRT(2*pi)*sigma*x) * e^(-log(x-mu)^2/2sigma^2)
* </pre>
*
*
* @param x The value.
* @param mu The mean.
* @param sigma The standard deviation.
* @return PDF of the given normal distribution at x.
*/
public static double pdf(double x, double mu, double sigma) {
if (x <= 0.) {
return 0.;
}
final double x_mu = Math.log(x) - mu;
final double sigmasq = sigma * sigma;
return 1 / (MathUtil.SQRTTWOPI * sigma * x) * Math.exp(-.5 * x_mu * x_mu / sigmasq);
}
/**
* Cumulative probability density function (CDF) of a normal distribution.
*
* @param x value to evaluate CDF at
* @param mu Mean value
* @param sigma Standard deviation.
* @return The CDF of the given normal distribution at x.
*/
public static double cdf(double x, double mu, double sigma) {
if (x <= 0.) {
return 0.;
}
return .5 * (1 + NormalDistribution.erf((Math.log(x) - mu) / (MathUtil.SQRT2 * sigma)));
}
/**
* Inverse cumulative probability density function (probit) of a normal
* distribution.
*
* @param x value to evaluate probit function at
* @param mu Mean value
* @param sigma Standard deviation.
* @return The probit of the given normal distribution at x.
*/
public static double quantile(double x, double mu, double sigma) {
return Math.exp(mu + sigma * NormalDistribution.standardNormalQuantile(x));
}
@Override
public double nextRandom() {
return Math.exp(logmean + random.nextGaussian() * logstddev) + shift;
}
@Override
public String toString() {
return "LogNormalDistribution(logmean=" + logmean + ", logstddev=" + logstddev + ", shift=" + shift + ")";
}
}
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