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) 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 .
*/
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution;
import de.lmu.ifi.dbs.elki.math.statistics.distribution.GeneralizedExtremeValueDistribution;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Estimate the parameters of a Generalized Extreme Value Distribution, using
* the methods of L-Moments (LMM).
*
* Reference:
*
* J. R. M. Hosking, J. R. Wallis, and E. F. Wood
* Estimation of the generalized extreme-value distribution by the method of
* probability-weighted moments.
* Technometrics 27.3
*
*
* @author Erich Schubert
*
* @apiviz.has GeneralizedExtremeValueDistribution
*/
@Reference(authors = "J.R.M. Hosking, J. R. Wallis, and E. F. Wood", title = "Estimation of the generalized extreme-value distribution by the method of probability-weighted moments.", booktitle = "Technometrics 27.3", url = "http://dx.doi.org/10.1080/00401706.1985.10488049")
public class GeneralizedExtremeValueLMMEstimator extends AbstractLMMEstimator {
/**
* Static instance.
*/
public static final GeneralizedExtremeValueLMMEstimator STATIC = new GeneralizedExtremeValueLMMEstimator();
/**
* Constants for fast rational approximations.
*/
private static final double //
A0 = 0.28377530, //
A1 = -1.21096399, //
A2 = -2.50728214, //
A3 = -1.13455566, //
A4 = -0.07138022;
private static final double //
B1 = 2.06189696, //
B2 = 1.31912239, //
B3 = 0.25077104;
private static final double //
C1 = 1.59921491, //
C2 = -0.48832213, //
C3 = 0.01573152, //
D1 = -0.64363929, //
D2 = 0.08985247;
/** Maximum number of iterations. */
static int MAXIT = 20;
/**
* Constructor. Private: use static instance.
*/
private GeneralizedExtremeValueLMMEstimator() {
super();
}
@Override
public int getNumMoments() {
return 3;
}
@Override
public GeneralizedExtremeValueDistribution estimateFromLMoments(double[] xmom) {
double t3 = xmom[2];
if (Math.abs(t3) < 1e-50 || (t3 >= 1.)) {
throw new ArithmeticException("Invalid moment estimation.");
}
// Approximation for t3 between 0 and 1:
double g;
if (t3 > 0.) {
double z = 1. - t3;
g = (-1. + z * (C1 + z * (C2 + z * C3))) / (1. + z * (D1 + z * D2));
// g: Almost zero?
if (Math.abs(g) < 1e-50) {
double k = 0;
double sigma = xmom[1] / MathUtil.LOG2;
double mu = xmom[0] - Math.E * sigma;
return new GeneralizedExtremeValueDistribution(mu, sigma, k);
}
} else {
// Approximation for t3 between -.8 and 0L:
g = (A0 + t3 * (A1 + t3 * (A2 + t3 * (A3 + t3 * A4)))) / (1. + t3 * (B1 + t3 * (B2 + t3 * B3)));
if (t3 < -.8) {
// Newton-Raphson iteration for t3 < -.8
if (t3 <= -.97) {
g = 1. - Math.log(1. + t3) / MathUtil.LOG2;
}
double t0 = .5 * (t3 + 3.);
for (int it = 1;; it++) {
double x2 = Math.pow(2., -g), xx2 = 1. - x2;
double x3 = Math.pow(3., -g), xx3 = 1. - x3;
double t = xx3 / xx2;
double deriv = (xx2 * x3 * MathUtil.LOG3 - xx3 * x2 * MathUtil.LOG2) / (xx2 * x2);
double oldg = g;
g -= (t - t0) / deriv;
if (Math.abs(g - oldg) < 1e-20 * g) {
break;
}
if (it >= MAXIT) {
throw new ArithmeticException("Newton-Raphson did not converge.");
}
}
}
}
double gam = Math.exp(GammaDistribution.logGamma(1. + g));
final double mu, sigma, k;
k = g;
sigma = xmom[1] * g / (gam * (1. - Math.pow(2., -g)));
mu = xmom[0] - sigma * (1. - gam) / g;
return new GeneralizedExtremeValueDistribution(mu, sigma, k);
}
@Override
public Class super GeneralizedExtremeValueDistribution> getDistributionClass() {
return GeneralizedExtremeValueDistribution.class;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected GeneralizedExtremeValueLMMEstimator makeInstance() {
return STATIC;
}
}
}