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.MathRuntimeException; 23 24 /** 25 * The default implementation of {@link ExponentialDistribution}. 26 * 27 * @version $Revision: 772119 $ $Date: 2009-05-06 05:43:28 -0400 (Wed, 06 May 2009) $ 28 */ 29 public class ExponentialDistributionImpl extends AbstractContinuousDistribution 30 implements ExponentialDistribution, Serializable { 31 32 /** Serializable version identifier */ 33 private static final long serialVersionUID = 2401296428283614780L; 34 35 /** The mean of this distribution. */ 36 private double mean; 37 38 /** 39 * Create a exponential distribution with the given mean. 40 * @param mean mean of this distribution. 41 */ 42 public ExponentialDistributionImpl(double mean) { 43 super(); 44 setMean(mean); 45 } 46 47 /** 48 * Modify the mean. 49 * @param mean the new mean. 50 * @throws IllegalArgumentException if <code>mean</code> is not positive. 51 */ 52 public void setMean(double mean) { 53 if (mean <= 0.0) { 54 throw MathRuntimeException.createIllegalArgumentException( 55 "mean must be positive ({0})", mean); 56 } 57 this.mean = mean; 58 } 59 60 /** 61 * Access the mean. 62 * @return the mean. 63 */ 64 public double getMean() { 65 return mean; 66 } 67 68 /** 69 * Return the probability density for a particular point. 70 * 71 * @param x The point at which the density should be computed. 72 * @return The pdf at point x. 73 */ 74 public double density(Double x) { 75 if (x < 0) { 76 return 0; 77 } 78 return Math.exp(-x / getMean()) / getMean(); 79 } 80 81 /** 82 * For this distribution, X, this method returns P(X < x). 83 * 84 * The implementation of this method is based on: 85 * <ul> 86 * <li> 87 * <a href="http://mathworld.wolfram.com/ExponentialDistribution.html"> 88 * Exponential Distribution</a>, equation (1).</li> 89 * </ul> 90 * 91 * @param x the value at which the CDF is evaluated. 92 * @return CDF for this distribution. 93 * @throws MathException if the cumulative probability can not be 94 * computed due to convergence or other numerical errors. 95 */ 96 public double cumulativeProbability(double x) throws MathException{ 97 double ret; 98 if (x <= 0.0) { 99 ret = 0.0; 100 } else { 101 ret = 1.0 - Math.exp(-x / getMean()); 102 } 103 return ret; 104 } 105 106 /** 107 * For this distribution, X, this method returns the critical point x, such 108 * that P(X < x) = <code>p</code>. 109 * <p> 110 * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY</code> for p=1.</p> 111 * 112 * @param p the desired probability 113 * @return x, such that P(X < x) = <code>p</code> 114 * @throws MathException if the inverse cumulative probability can not be 115 * computed due to convergence or other numerical errors. 116 * @throws IllegalArgumentException if p < 0 or p > 1. 117 */ 118 @Override 119 public double inverseCumulativeProbability(double p) throws MathException { 120 double ret; 121 122 if (p < 0.0 || p > 1.0) { 123 throw MathRuntimeException.createIllegalArgumentException( 124 "{0} out of [{1}, {2}] range", p, 0.0, 1.0); 125 } else if (p == 1.0) { 126 ret = Double.POSITIVE_INFINITY; 127 } else { 128 ret = -getMean() * Math.log(1.0 - p); 129 } 130 131 return ret; 132 } 133 134 /** 135 * Access the domain value lower bound, based on <code>p</code>, used to 136 * bracket a CDF root. 137 * 138 * @param p the desired probability for the critical value 139 * @return domain value lower bound, i.e. 140 * P(X < <i>lower bound</i>) < <code>p</code> 141 */ 142 @Override 143 protected double getDomainLowerBound(double p) { 144 return 0; 145 } 146 147 /** 148 * Access the domain value upper bound, based on <code>p</code>, used to 149 * bracket a CDF root. 150 * 151 * @param p the desired probability for the critical value 152 * @return domain value upper bound, i.e. 153 * P(X < <i>upper bound</i>) > <code>p</code> 154 */ 155 @Override 156 protected double getDomainUpperBound(double p) { 157 // NOTE: exponential is skewed to the left 158 // NOTE: therefore, P(X < μ) > .5 159 160 if (p < .5) { 161 // use mean 162 return getMean(); 163 } else { 164 // use max 165 return Double.MAX_VALUE; 166 } 167 } 168 169 /** 170 * Access the initial domain value, based on <code>p</code>, used to 171 * bracket a CDF root. 172 * 173 * @param p the desired probability for the critical value 174 * @return initial domain value 175 */ 176 @Override 177 protected double getInitialDomain(double p) { 178 // TODO: try to improve on this estimate 179 // TODO: what should really happen here is not derive from AbstractContinuousDistribution 180 // TODO: because the inverse cumulative distribution is simple. 181 // Exponential is skewed to the left, therefore, P(X < μ) > .5 182 if (p < .5) { 183 // use 1/2 mean 184 return getMean() * .5; 185 } else { 186 // use mean 187 return getMean(); 188 } 189 } 190 }