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/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math.distribution; import java.io.Serializable; import org.apache.commons.math.MathException; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.exception.util.LocalizedFormats; import org.apache.commons.math.special.Gamma; import org.apache.commons.math.util.FastMath; /** * The default implementation of {@link GammaDistribution}. * * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ */ public class GammaDistributionImpl extends AbstractContinuousDistribution implements GammaDistribution, Serializable { /** * Default inverse cumulative probability accuracy * @since 2.1 */ public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9; /** Serializable version identifier */ private static final long serialVersionUID = -3239549463135430361L; /** The shape parameter. */ private double alpha; /** The scale parameter. */ private double beta; /** Inverse cumulative probability accuracy */ private final double solverAbsoluteAccuracy; /** * Create a new gamma distribution with the given alpha and beta values. * @param alpha the shape parameter. * @param beta the scale parameter. */ public GammaDistributionImpl(double alpha, double beta) { this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Create a new gamma distribution with the given alpha and beta values. * @param alpha the shape parameter. * @param beta the scale parameter. * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) * @since 2.1 */ public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) { super(); setAlphaInternal(alpha); setBetaInternal(beta); solverAbsoluteAccuracy = inverseCumAccuracy; } /** * For this distribution, X, this method returns P(X < x). * * The implementation of this method is based on: * <ul> * <li> * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> * Chi-Squared Distribution</a>, equation (9).</li> * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>. * Belmont, CA: Duxbury Press.</li> * </ul> * * @param x the value at which the CDF is evaluated. * @return CDF for this distribution. * @throws MathException if the cumulative probability can not be * computed due to convergence or other numerical errors. */ public double cumulativeProbability(double x) throws MathException { double ret; if (x <= 0.0) { ret = 0.0; } else { ret = Gamma.regularizedGammaP(alpha, x / beta); } return ret; } /** * For this distribution, X, this method returns the critical point x, such * that P(X < x) = <code>p</code>. * <p> * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> * * @param p the desired probability * @return x, such that P(X < x) = <code>p</code> * @throws MathException if the inverse cumulative probability can not be * computed due to convergence or other numerical errors. * @throws IllegalArgumentException if <code>p</code> is not a valid * probability. */ @Override public double inverseCumulativeProbability(final double p) throws MathException { if (p == 0) { return 0d; } if (p == 1) { return Double.POSITIVE_INFINITY; } return super.inverseCumulativeProbability(p); } /** * Modify the shape parameter, alpha. * @param alpha the new shape parameter. * @throws IllegalArgumentException if <code>alpha</code> is not positive. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setAlpha(double alpha) { setAlphaInternal(alpha); } /** * Modify the shape parameter, alpha. * @param newAlpha the new shape parameter. * @throws IllegalArgumentException if <code>newAlpha</code> is not positive. */ private void setAlphaInternal(double newAlpha) { if (newAlpha <= 0.0) { throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_ALPHA, newAlpha); } this.alpha = newAlpha; } /** * Access the shape parameter, alpha * @return alpha. */ public double getAlpha() { return alpha; } /** * Modify the scale parameter, beta. * @param newBeta the new scale parameter. * @throws IllegalArgumentException if <code>newBeta</code> is not positive. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setBeta(double newBeta) { setBetaInternal(newBeta); } /** * Modify the scale parameter, beta. * @param newBeta the new scale parameter. * @throws IllegalArgumentException if <code>newBeta</code> is not positive. */ private void setBetaInternal(double newBeta) { if (newBeta <= 0.0) { throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_BETA, newBeta); } this.beta = newBeta; } /** * Access the scale parameter, beta * @return beta. */ public double getBeta() { return beta; } /** * Returns the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. */ @Override public double density(double x) { if (x < 0) return 0; return FastMath.pow(x / beta, alpha - 1) / beta * FastMath.exp(-x / beta) / FastMath.exp(Gamma.logGamma(alpha)); } /** * Return the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. * @deprecated */ @Deprecated public double density(Double x) { return density(x.doubleValue()); } /** * Access the domain value lower bound, based on <code>p</code>, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return domain value lower bound, i.e. * P(X < <i>lower bound</i>) < <code>p</code> */ @Override protected double getDomainLowerBound(double p) { // TODO: try to improve on this estimate return Double.MIN_VALUE; } /** * Access the domain value upper bound, based on <code>p</code>, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return domain value upper bound, i.e. * P(X < <i>upper bound</i>) > <code>p</code> */ @Override protected double getDomainUpperBound(double p) { // TODO: try to improve on this estimate // NOTE: gamma is skewed to the left // NOTE: therefore, P(X < μ) > .5 double ret; if (p < .5) { // use mean ret = alpha * beta; } else { // use max value ret = Double.MAX_VALUE; } return ret; } /** * Access the initial domain value, based on <code>p</code>, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return initial domain value */ @Override protected double getInitialDomain(double p) { // TODO: try to improve on this estimate // Gamma is skewed to the left, therefore, P(X < μ) > .5 double ret; if (p < .5) { // use 1/2 mean ret = alpha * beta * .5; } else { // use mean ret = alpha * beta; } return ret; } /** * Return the absolute accuracy setting of the solver used to estimate * inverse cumulative probabilities. * * @return the solver absolute accuracy * @since 2.1 */ @Override protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } /** * Returns the upper bound of the support for the distribution. * * The lower bound of the support is always 0, regardless of the parameters. * * @return lower bound of the support (always 0) * @since 2.2 */ public double getSupportLowerBound() { return 0; } /** * Returns the upper bound of the support for the distribution. * * The upper bound of the support is always positive infinity, * regardless of the parameters. * * @return upper bound of the support (always Double.POSITIVE_INFINITY) * @since 2.2 */ public double getSupportUpperBound() { return Double.POSITIVE_INFINITY; } /** * Returns the mean. * * For shape parameter <code>alpha</code> and scale * parameter <code>beta</code>, the mean is * <code>alpha * beta</code> * * @return the mean * @since 2.2 */ public double getNumericalMean() { return getAlpha() * getBeta(); } /** * Returns the variance. * * For shape parameter <code>alpha</code> and scale * parameter <code>beta</code>, the variance is * <code>alpha * beta^2</code> * * @return the variance * @since 2.2 */ public double getNumericalVariance() { final double b = getBeta(); return getAlpha() * b * b; } }