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package de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator;
/*
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 de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Estimate distribution parameters using the method by Choi and Wette.
*
* Reference:
* <p>
* Maximum likelihood estimation of the parameters of the gamma distribution and
* their bias<br />
* S. C. Choi, R. Wette<br />
* in: Technometrics
* </p>
*
* @author Erich Schubert
* @since 0.6.0
*
* @apiviz.has GammaDistribution - - estimates
*/
@Reference(title = "Maximum likelihood estimation of the parameters of the gamma distribution and their bias", authors = "S. C. Choi, R. Wette", booktitle = "Technometrics", url = "http://www.jstor.org/stable/10.2307/1266892")
public class GammaChoiWetteEstimator implements DistributionEstimator<GammaDistribution> {
/**
* Static estimation, using iterative refinement.
*/
public static final GammaChoiWetteEstimator STATIC = new GammaChoiWetteEstimator();
/**
* Private constructor.
*/
private GammaChoiWetteEstimator() {
// Do not instantiate - use static class
}
@Override
public <A> GammaDistribution estimate(A data, NumberArrayAdapter<?, A> adapter) {
final int len = adapter.size(data);
double meanx = 0, meanlogx = 0;
for (int i = 0; i < len; i++) {
final double val = adapter.getDouble(data, i);
if (val <= 0 || Double.isInfinite(val) || Double.isNaN(val)) {
continue;
}
final double logx = (val > 0) ? Math.log(val) : meanlogx;
final double deltax = val - meanx;
final double deltalogx = logx - meanlogx;
meanx += deltax / (i + 1.);
meanlogx += deltalogx / (i + 1.);
}
// Initial approximation
final double logmeanx = (meanx > 0) ? Math.log(meanx) : meanlogx;
final double diff = logmeanx - meanlogx;
double k = (3 - diff + Math.sqrt((diff - 3) * (diff - 3) + 24 * diff)) / (12 * diff);
// Refine via newton iteration, based on Choi and Wette equation
while (true) {
double kdelta = (Math.log(k) - GammaDistribution.digamma(k) - diff) / (1 / k - GammaDistribution.trigamma(k));
if (Math.abs(kdelta) / k < 1E-8 || !(kdelta < Double.POSITIVE_INFINITY)) {
break;
}
k += kdelta;
}
// Estimate theta:
final double theta = k / meanx;
if (!(k > 0.0) || !(theta > 0.0)) {
throw new ArithmeticException("Gamma estimation produced non-positive parameter values: k=" + k + " theta=" + theta);
}
return new GammaDistribution(k, theta);
}
@Override
public Class<? super GammaDistribution> getDistributionClass() {
return GammaDistribution.class;
}
@Override
public String toString() {
return this.getClass().getSimpleName();
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected GammaChoiWetteEstimator makeInstance() {
return STATIC;
}
}
}
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