001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 package org.apache.commons.math.distribution; 018 019 import java.io.Serializable; 020 021 import org.apache.commons.math.MathException; 022 import org.apache.commons.math.MathRuntimeException; 023 import org.apache.commons.math.special.Gamma; 024 025 /** 026 * The default implementation of {@link GammaDistribution}. 027 * 028 * @version $Revision: 772119 $ $Date: 2009-05-06 05:43:28 -0400 (Wed, 06 May 2009) $ 029 */ 030 public class GammaDistributionImpl extends AbstractContinuousDistribution 031 implements GammaDistribution, Serializable { 032 033 /** Serializable version identifier */ 034 private static final long serialVersionUID = -3239549463135430361L; 035 036 /** The shape parameter. */ 037 private double alpha; 038 039 /** The scale parameter. */ 040 private double beta; 041 042 /** 043 * Create a new gamma distribution with the given alpha and beta values. 044 * @param alpha the shape parameter. 045 * @param beta the scale parameter. 046 */ 047 public GammaDistributionImpl(double alpha, double beta) { 048 super(); 049 setAlpha(alpha); 050 setBeta(beta); 051 } 052 053 /** 054 * For this distribution, X, this method returns P(X < x). 055 * 056 * The implementation of this method is based on: 057 * <ul> 058 * <li> 059 * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> 060 * Chi-Squared Distribution</a>, equation (9).</li> 061 * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>. 062 * Belmont, CA: Duxbury Press.</li> 063 * </ul> 064 * 065 * @param x the value at which the CDF is evaluated. 066 * @return CDF for this distribution. 067 * @throws MathException if the cumulative probability can not be 068 * computed due to convergence or other numerical errors. 069 */ 070 public double cumulativeProbability(double x) throws MathException{ 071 double ret; 072 073 if (x <= 0.0) { 074 ret = 0.0; 075 } else { 076 ret = Gamma.regularizedGammaP(getAlpha(), x / getBeta()); 077 } 078 079 return ret; 080 } 081 082 /** 083 * For this distribution, X, this method returns the critical point x, such 084 * that P(X < x) = <code>p</code>. 085 * <p> 086 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 087 * 088 * @param p the desired probability 089 * @return x, such that P(X < x) = <code>p</code> 090 * @throws MathException if the inverse cumulative probability can not be 091 * computed due to convergence or other numerical errors. 092 * @throws IllegalArgumentException if <code>p</code> is not a valid 093 * probability. 094 */ 095 @Override 096 public double inverseCumulativeProbability(final double p) 097 throws MathException { 098 if (p == 0) { 099 return 0d; 100 } 101 if (p == 1) { 102 return Double.POSITIVE_INFINITY; 103 } 104 return super.inverseCumulativeProbability(p); 105 } 106 107 /** 108 * Modify the shape parameter, alpha. 109 * @param alpha the new shape parameter. 110 * @throws IllegalArgumentException if <code>alpha</code> is not positive. 111 */ 112 public void setAlpha(double alpha) { 113 if (alpha <= 0.0) { 114 throw MathRuntimeException.createIllegalArgumentException( 115 "alpha must be positive ({0})", 116 alpha); 117 } 118 this.alpha = alpha; 119 } 120 121 /** 122 * Access the shape parameter, alpha 123 * @return alpha. 124 */ 125 public double getAlpha() { 126 return alpha; 127 } 128 129 /** 130 * Modify the scale parameter, beta. 131 * @param beta the new scale parameter. 132 * @throws IllegalArgumentException if <code>beta</code> is not positive. 133 */ 134 public void setBeta(double beta) { 135 if (beta <= 0.0) { 136 throw MathRuntimeException.createIllegalArgumentException( 137 "beta must be positive ({0})", 138 beta); 139 } 140 this.beta = beta; 141 } 142 143 /** 144 * Access the scale parameter, beta 145 * @return beta. 146 */ 147 public double getBeta() { 148 return beta; 149 } 150 151 /** 152 * Return the probability density for a particular point. 153 * 154 * @param x The point at which the density should be computed. 155 * @return The pdf at point x. 156 */ 157 public double density(Double x) { 158 if (x < 0) return 0; 159 return Math.pow(x / getBeta(), getAlpha() - 1) / getBeta() * Math.exp(-x / getBeta()) / Math.exp(Gamma.logGamma(getAlpha())); 160 } 161 162 /** 163 * Access the domain value lower bound, based on <code>p</code>, used to 164 * bracket a CDF root. This method is used by 165 * {@link #inverseCumulativeProbability(double)} to find critical values. 166 * 167 * @param p the desired probability for the critical value 168 * @return domain value lower bound, i.e. 169 * P(X < <i>lower bound</i>) < <code>p</code> 170 */ 171 @Override 172 protected double getDomainLowerBound(double p) { 173 // TODO: try to improve on this estimate 174 return Double.MIN_VALUE; 175 } 176 177 /** 178 * Access the domain value upper bound, based on <code>p</code>, used to 179 * bracket a CDF root. This method is used by 180 * {@link #inverseCumulativeProbability(double)} to find critical values. 181 * 182 * @param p the desired probability for the critical value 183 * @return domain value upper bound, i.e. 184 * P(X < <i>upper bound</i>) > <code>p</code> 185 */ 186 @Override 187 protected double getDomainUpperBound(double p) { 188 // TODO: try to improve on this estimate 189 // NOTE: gamma is skewed to the left 190 // NOTE: therefore, P(X < μ) > .5 191 192 double ret; 193 194 if (p < .5) { 195 // use mean 196 ret = getAlpha() * getBeta(); 197 } else { 198 // use max value 199 ret = Double.MAX_VALUE; 200 } 201 202 return ret; 203 } 204 205 /** 206 * Access the initial domain value, based on <code>p</code>, used to 207 * bracket a CDF root. This method is used by 208 * {@link #inverseCumulativeProbability(double)} to find critical values. 209 * 210 * @param p the desired probability for the critical value 211 * @return initial domain value 212 */ 213 @Override 214 protected double getInitialDomain(double p) { 215 // TODO: try to improve on this estimate 216 // Gamma is skewed to the left, therefore, P(X < μ) > .5 217 218 double ret; 219 220 if (p < .5) { 221 // use 1/2 mean 222 ret = getAlpha() * getBeta() * .5; 223 } else { 224 // use mean 225 ret = getAlpha() * getBeta(); 226 } 227 228 return ret; 229 } 230 }