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; 023 024 /** 025 * The default implementation of {@link ExponentialDistribution}. 026 * 027 * @version $Revision: 772119 $ $Date: 2009-05-06 05:43:28 -0400 (Wed, 06 May 2009) $ 028 */ 029 public class ExponentialDistributionImpl extends AbstractContinuousDistribution 030 implements ExponentialDistribution, Serializable { 031 032 /** Serializable version identifier */ 033 private static final long serialVersionUID = 2401296428283614780L; 034 035 /** The mean of this distribution. */ 036 private double mean; 037 038 /** 039 * Create a exponential distribution with the given mean. 040 * @param mean mean of this distribution. 041 */ 042 public ExponentialDistributionImpl(double mean) { 043 super(); 044 setMean(mean); 045 } 046 047 /** 048 * Modify the mean. 049 * @param mean the new mean. 050 * @throws IllegalArgumentException if <code>mean</code> is not positive. 051 */ 052 public void setMean(double mean) { 053 if (mean <= 0.0) { 054 throw MathRuntimeException.createIllegalArgumentException( 055 "mean must be positive ({0})", mean); 056 } 057 this.mean = mean; 058 } 059 060 /** 061 * Access the mean. 062 * @return the mean. 063 */ 064 public double getMean() { 065 return mean; 066 } 067 068 /** 069 * Return the probability density for a particular point. 070 * 071 * @param x The point at which the density should be computed. 072 * @return The pdf at point x. 073 */ 074 public double density(Double x) { 075 if (x < 0) { 076 return 0; 077 } 078 return Math.exp(-x / getMean()) / getMean(); 079 } 080 081 /** 082 * For this distribution, X, this method returns P(X < x). 083 * 084 * The implementation of this method is based on: 085 * <ul> 086 * <li> 087 * <a href="http://mathworld.wolfram.com/ExponentialDistribution.html"> 088 * Exponential Distribution</a>, equation (1).</li> 089 * </ul> 090 * 091 * @param x the value at which the CDF is evaluated. 092 * @return CDF for this distribution. 093 * @throws MathException if the cumulative probability can not be 094 * computed due to convergence or other numerical errors. 095 */ 096 public double cumulativeProbability(double x) throws MathException{ 097 double ret; 098 if (x <= 0.0) { 099 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 }