1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math.distribution; 18 19 import java.io.Serializable; 20 21 import org.apache.commons.math.MathException; 22 import org.apache.commons.math.special.Gamma; 23 24 /** 25 * The default implementation of {@link GammaDistribution}. 26 * 27 * @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $ 28 */ 29 public class GammaDistributionImpl extends AbstractContinuousDistribution 30 implements GammaDistribution, Serializable { 31 32 /** Serializable version identifier */ 33 private static final long serialVersionUID = -3239549463135430361L; 34 35 /** The shape parameter. */ 36 private double alpha; 37 38 /** The scale parameter. */ 39 private double beta; 40 41 /** 42 * Create a new gamma distribution with the given alpha and beta values. 43 * @param alpha the shape parameter. 44 * @param beta the scale parameter. 45 */ 46 public GammaDistributionImpl(double alpha, double beta) { 47 super(); 48 setAlpha(alpha); 49 setBeta(beta); 50 } 51 52 /** 53 * For this disbution, X, this method returns P(X < x). 54 * 55 * The implementation of this method is based on: 56 * <ul> 57 * <li> 58 * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html"> 59 * Chi-Squared Distribution</a>, equation (9).</li> 60 * <li>Casella, G., & Berger, R. (1990). <i>Statistical Inference</i>. 61 * Belmont, CA: Duxbury Press.</li> 62 * </ul> 63 * 64 * @param x the value at which the CDF is evaluated. 65 * @return CDF for this distribution. 66 * @throws MathException if the cumulative probability can not be 67 * computed due to convergence or other numerical errors. 68 */ 69 public double cumulativeProbability(double x) throws MathException{ 70 double ret; 71 72 if (x <= 0.0) { 73 ret = 0.0; 74 } else { 75 ret = Gamma.regularizedGammaP(getAlpha(), x / getBeta()); 76 } 77 78 return ret; 79 } 80 81 /** 82 * For this distribution, X, this method returns the critical point x, such 83 * that P(X < x) = <code>p</code>. 84 * <p> 85 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 86 * 87 * @param p the desired probability 88 * @return x, such that P(X < x) = <code>p</code> 89 * @throws MathException if the inverse cumulative probability can not be 90 * computed due to convergence or other numerical errors. 91 * @throws IllegalArgumentException if <code>p</code> is not a valid 92 * probability. 93 */ 94 public double inverseCumulativeProbability(final double p) 95 throws MathException { 96 if (p == 0) { 97 return 0d; 98 } 99 if (p == 1) { 100 return Double.POSITIVE_INFINITY; 101 } 102 return super.inverseCumulativeProbability(p); 103 } 104 105 /** 106 * Modify the shape parameter, alpha. 107 * @param alpha the new shape parameter. 108 * @throws IllegalArgumentException if <code>alpha</code> is not positive. 109 */ 110 public void setAlpha(double alpha) { 111 if (alpha <= 0.0) { 112 throw new IllegalArgumentException("alpha must be positive"); 113 } 114 this.alpha = alpha; 115 } 116 117 /** 118 * Access the shape parameter, alpha 119 * @return alpha. 120 */ 121 public double getAlpha() { 122 return alpha; 123 } 124 125 /** 126 * Modify the scale parameter, beta. 127 * @param beta the new scale parameter. 128 * @throws IllegalArgumentException if <code>beta</code> is not positive. 129 */ 130 public void setBeta(double beta) { 131 if (beta <= 0.0) { 132 throw new IllegalArgumentException("beta must be positive"); 133 } 134 this.beta = beta; 135 } 136 137 /** 138 * Access the scale parameter, beta 139 * @return beta. 140 */ 141 public double getBeta() { 142 return beta; 143 } 144 145 /** 146 * Access the domain value lower bound, based on <code>p</code>, used to 147 * bracket a CDF root. This method is used by 148 * {@link #inverseCumulativeProbability(double)} to find critical values. 149 * 150 * @param p the desired probability for the critical value 151 * @return domain value lower bound, i.e. 152 * P(X < <i>lower bound</i>) < <code>p</code> 153 */ 154 protected double getDomainLowerBound(double p) { 155 // TODO: try to improve on this estimate 156 return Double.MIN_VALUE; 157 } 158 159 /** 160 * Access the domain value upper bound, based on <code>p</code>, used to 161 * bracket a CDF root. This method is used by 162 * {@link #inverseCumulativeProbability(double)} to find critical values. 163 * 164 * @param p the desired probability for the critical value 165 * @return domain value upper bound, i.e. 166 * P(X < <i>upper bound</i>) > <code>p</code> 167 */ 168 protected double getDomainUpperBound(double p) { 169 // TODO: try to improve on this estimate 170 // NOTE: gamma is skewed to the left 171 // NOTE: therefore, P(X < μ) > .5 172 173 double ret; 174 175 if (p < .5) { 176 // use mean 177 ret = getAlpha() * getBeta(); 178 } else { 179 // use max value 180 ret = Double.MAX_VALUE; 181 } 182 183 return ret; 184 } 185 186 /** 187 * Access the initial domain value, based on <code>p</code>, used to 188 * bracket a CDF root. This method is used by 189 * {@link #inverseCumulativeProbability(double)} to find critical values. 190 * 191 * @param p the desired probability for the critical value 192 * @return initial domain value 193 */ 194 protected double getInitialDomain(double p) { 195 // TODO: try to improve on this estimate 196 // Gamma is skewed to the left, therefore, P(X < μ) > .5 197 198 double ret; 199 200 if (p < .5) { 201 // use 1/2 mean 202 ret = getAlpha() * getBeta() * .5; 203 } else { 204 // use mean 205 ret = getAlpha() * getBeta(); 206 } 207 208 return ret; 209 } 210 }