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 /** 026 * Base class for integer-valued discrete distributions. Default 027 * implementations are provided for some of the methods that do not vary 028 * from distribution to distribution. 029 * 030 * @version $Revision: 772119 $ $Date: 2009-05-06 05:43:28 -0400 (Wed, 06 May 2009) $ 031 */ 032 public abstract class AbstractIntegerDistribution extends AbstractDistribution 033 implements IntegerDistribution, Serializable { 034 035 /** Serializable version identifier */ 036 private static final long serialVersionUID = -1146319659338487221L; 037 038 /** 039 * Default constructor. 040 */ 041 protected AbstractIntegerDistribution() { 042 super(); 043 } 044 045 /** 046 * For a random variable X whose values are distributed according 047 * to this distribution, this method returns P(X ≤ x). In other words, 048 * this method represents the (cumulative) distribution function, or 049 * CDF, for this distribution. 050 * <p> 051 * If <code>x</code> does not represent an integer value, the CDF is 052 * evaluated at the greatest integer less than x. 053 * 054 * @param x the value at which the distribution function is evaluated. 055 * @return cumulative probability that a random variable with this 056 * distribution takes a value less than or equal to <code>x</code> 057 * @throws MathException if the cumulative probability can not be 058 * computed due to convergence or other numerical errors. 059 */ 060 public double cumulativeProbability(double x) throws MathException { 061 return cumulativeProbability((int) Math.floor(x)); 062 } 063 064 /** 065 * For a random variable X whose values are distributed according 066 * to this distribution, this method returns P(x0 ≤ X ≤ x1). 067 * 068 * @param x0 the (inclusive) lower bound 069 * @param x1 the (inclusive) upper bound 070 * @return the probability that a random variable with this distribution 071 * will take a value between <code>x0</code> and <code>x1</code>, 072 * including the endpoints. 073 * @throws MathException if the cumulative probability can not be 074 * computed due to convergence or other numerical errors. 075 * @throws IllegalArgumentException if <code>x0 > x1</code> 076 */ 077 @Override 078 public double cumulativeProbability(double x0, double x1) 079 throws MathException { 080 if (x0 > x1) { 081 throw MathRuntimeException.createIllegalArgumentException( 082 "lower endpoint ({0}) must be less than or equal to upper endpoint ({1})", 083 x0, x1); 084 } 085 if (Math.floor(x0) < x0) { 086 return cumulativeProbability(((int) Math.floor(x0)) + 1, 087 (int) Math.floor(x1)); // don't want to count mass below x0 088 } else { // x0 is mathematical integer, so use as is 089 return cumulativeProbability((int) Math.floor(x0), 090 (int) Math.floor(x1)); 091 } 092 } 093 094 /** 095 * For a random variable X whose values are distributed according 096 * to this distribution, this method returns P(X ≤ x). In other words, 097 * this method represents the probability distribution function, or PDF, 098 * for this distribution. 099 * 100 * @param x the value at which the PDF is evaluated. 101 * @return PDF for this distribution. 102 * @throws MathException if the cumulative probability can not be 103 * computed due to convergence or other numerical errors. 104 */ 105 abstract public double cumulativeProbability(int x) throws MathException; 106 107 /** 108 * For a random variable X whose values are distributed according 109 * to this distribution, this method returns P(X = x). In other words, this 110 * method represents the probability mass function, or PMF, for the distribution. 111 * <p> 112 * If <code>x</code> does not represent an integer value, 0 is returned. 113 * 114 * @param x the value at which the probability density function is evaluated 115 * @return the value of the probability density function at x 116 */ 117 public double probability(double x) { 118 double fl = Math.floor(x); 119 if (fl == x) { 120 return this.probability((int) x); 121 } else { 122 return 0; 123 } 124 } 125 126 /** 127 * For a random variable X whose values are distributed according 128 * to this distribution, this method returns P(x0 ≤ X ≤ x1). 129 * 130 * @param x0 the inclusive, lower bound 131 * @param x1 the inclusive, upper bound 132 * @return the cumulative probability. 133 * @throws MathException if the cumulative probability can not be 134 * computed due to convergence or other numerical errors. 135 * @throws IllegalArgumentException if x0 > x1 136 */ 137 public double cumulativeProbability(int x0, int x1) throws MathException { 138 if (x0 > x1) { 139 throw MathRuntimeException.createIllegalArgumentException( 140 "lower endpoint ({0}) must be less than or equal to upper endpoint ({1})", 141 x0, x1); 142 } 143 return cumulativeProbability(x1) - cumulativeProbability(x0 - 1); 144 } 145 146 /** 147 * For a random variable X whose values are distributed according 148 * to this distribution, this method returns the largest x, such 149 * that P(X ≤ x) ≤ <code>p</code>. 150 * 151 * @param p the desired probability 152 * @return the largest x such that P(X ≤ x) <= p 153 * @throws MathException if the inverse cumulative probability can not be 154 * computed due to convergence or other numerical errors. 155 * @throws IllegalArgumentException if p < 0 or p > 1 156 */ 157 public int inverseCumulativeProbability(final double p) throws MathException{ 158 if (p < 0.0 || p > 1.0) { 159 throw MathRuntimeException.createIllegalArgumentException( 160 "{0} out of [{1}, {2}] range", p, 0.0, 1.0); 161 } 162 163 // by default, do simple bisection. 164 // subclasses can override if there is a better method. 165 int x0 = getDomainLowerBound(p); 166 int x1 = getDomainUpperBound(p); 167 double pm; 168 while (x0 < x1) { 169 int xm = x0 + (x1 - x0) / 2; 170 pm = cumulativeProbability(xm); 171 if (pm > p) { 172 // update x1 173 if (xm == x1) { 174 // this can happen with integer division 175 // simply decrement x1 176 --x1; 177 } else { 178 // update x1 normally 179 x1 = xm; 180 } 181 } else { 182 // update x0 183 if (xm == x0) { 184 // this can happen with integer division 185 // simply increment x0 186 ++x0; 187 } else { 188 // update x0 normally 189 x0 = xm; 190 } 191 } 192 } 193 194 // insure x0 is the correct critical point 195 pm = cumulativeProbability(x0); 196 while (pm > p) { 197 --x0; 198 pm = cumulativeProbability(x0); 199 } 200 201 return x0; 202 } 203 204 /** 205 * Access the domain value lower bound, based on <code>p</code>, used to 206 * bracket a PDF root. This method is used by 207 * {@link #inverseCumulativeProbability(double)} to find critical values. 208 * 209 * @param p the desired probability for the critical value 210 * @return domain value lower bound, i.e. 211 * P(X < <i>lower bound</i>) < <code>p</code> 212 */ 213 protected abstract int getDomainLowerBound(double p); 214 215 /** 216 * Access the domain value upper bound, based on <code>p</code>, used to 217 * bracket a PDF root. This method is used by 218 * {@link #inverseCumulativeProbability(double)} to find critical values. 219 * 220 * @param p the desired probability for the critical value 221 * @return domain value upper bound, i.e. 222 * P(X < <i>upper bound</i>) > <code>p</code> 223 */ 224 protected abstract int getDomainUpperBound(double p); 225 }