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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;
+
+/**
+ * Generalized Gaussian distribution by adding a skew term, similar to lognormal
+ * distributions.
+ *
+ * This is one kind of generalized normal distributions. Note that there are
+ * multiple that go by the name of a "Generalized Normal Distribution".
+ *
+ * @author Erich Schubert
+ */
+public class SkewGeneralizedNormalDistribution implements Distribution {
+ /**
+ * Mean value for the generator
+ */
+ private double mean;
+
+ /**
+ * Standard deviation
+ */
+ private double stddev;
+
+ /**
+ * Skew.
+ */
+ private double skew;
+
+ /**
+ * The random generator.
+ */
+ private Random random;
+
+ /**
+ * Constructor for Gaussian distribution
+ *
+ * @param mean Mean
+ * @param stddev Standard Deviation
+ * @param skew Skew
+ * @param random Random generator
+ */
+ public SkewGeneralizedNormalDistribution(double mean, double stddev, double skew, Random random) {
+ super();
+ this.mean = mean;
+ this.stddev = stddev;
+ this.skew = skew;
+ this.random = random;
+ }
+
+ /**
+ * Constructor for Gaussian distribution
+ *
+ * @param mean Mean
+ * @param stddev Standard Deviation
+ * @param skew Skew
+ */
+ public SkewGeneralizedNormalDistribution(double mean, double stddev, double skew) {
+ this(mean, stddev, skew, null);
+ }
+
+ @Override
+ public double pdf(double val) {
+ return pdf(val, mean, stddev, skew);
+ }
+
+ @Override
+ public double cdf(double val) {
+ return cdf(val, mean, stddev, skew);
+ }
+
+ @Override
+ public double quantile(double q) {
+ return quantile(q, mean, stddev, skew);
+ }
+
+ @Override
+ public double nextRandom() {
+ double y = random.nextGaussian();
+ if (Math.abs(skew) > 0.) {
+ y = (1. - Math.exp(-skew * y)) / skew;
+ }
+ return mean + stddev * y;
+
+ }
+
+ @Override
+ public String toString() {
+ return "SkewNormalDistribution(mean=" + mean + ", stddev=" + stddev + ", skew=" + skew + ")";
+ }
+
+ /**
+ * Probability density function of the skewed normal distribution.
+ *
+ * @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, double skew) {
+ x = (x - mu) / sigma;
+ if (Math.abs(skew) > 0.) {
+ x = -Math.log(1. - skew * x) / skew;
+ }
+ return MathUtil.SQRTHALF * Math.exp(-.5 * x * x) / sigma / (1 - skew * x);
+ }
+
+ /**
+ * 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, double skew) {
+ x = (x - mu) / sigma;
+ if (Math.abs(skew) > 0.) {
+ double tmp = 1 - skew * x;
+ if (tmp < 1e-15) {
+ return (skew < 0.) ? 0. : 1.;
+ }
+ x = -Math.log(tmp) / skew;
+ }
+ return .5 + .5 * NormalDistribution.erf(x * MathUtil.SQRTHALF);
+ }
+
+ /**
+ * 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, double skew) {
+ x = NormalDistribution.standardNormalQuantile(x);
+ if (Math.abs(skew) > 0.) {
+ x = (1. - Math.exp(-skew * x)) / skew;
+ }
+ return mu + sigma * x;
+ }
+}