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 23 24 /** 25 * Base class for integer-valued discrete distributions. Default 26 * implementations are provided for some of the methods that do not vary 27 * from distribution to distribution. 28 * 29 * @version $Revision: 620368 $ $Date: 2008-02-10 18:04:48 -0700 (Sun, 10 Feb 2008) $ 30 */ 31 public abstract class AbstractIntegerDistribution extends AbstractDistribution 32 implements IntegerDistribution, Serializable { 33 34 /** Serializable version identifier */ 35 private static final long serialVersionUID = -1146319659338487221L; 36 37 /** 38 * Default constructor. 39 */ 40 protected AbstractIntegerDistribution() { 41 super(); 42 } 43 44 /** 45 * For a random variable X whose values are distributed according 46 * to this distribution, this method returns P(X ≤ x). In other words, 47 * this method represents the (cumulative) distribution function, or 48 * CDF, for this distribution. 49 * <p> 50 * If <code>x</code> does not represent an integer value, the CDF is 51 * evaluated at the greatest integer less than x. 52 * 53 * @param x the value at which the distribution function is evaluated. 54 * @return cumulative probability that a random variable with this 55 * distribution takes a value less than or equal to <code>x</code> 56 * @throws MathException if the cumulative probability can not be 57 * computed due to convergence or other numerical errors. 58 */ 59 public double cumulativeProbability(double x) throws MathException { 60 return cumulativeProbability((int) Math.floor(x)); 61 } 62 63 /** 64 * For a random variable X whose values are distributed according 65 * to this distribution, this method returns P(x0 ≤ X ≤ x1). 66 * 67 * @param x0 the (inclusive) lower bound 68 * @param x1 the (inclusive) upper bound 69 * @return the probability that a random variable with this distribution 70 * will take a value between <code>x0</code> and <code>x1</code>, 71 * including the endpoints. 72 * @throws MathException if the cumulative probability can not be 73 * computed due to convergence or other numerical errors. 74 * @throws IllegalArgumentException if <code>x0 > x1</code> 75 */ 76 public double cumulativeProbability(double x0, double x1) 77 throws MathException { 78 if (x0 > x1) { 79 throw new IllegalArgumentException 80 ("lower endpoint must be less than or equal to upper endpoint"); 81 } 82 if (Math.floor(x0) < x0) { 83 return cumulativeProbability(((int) Math.floor(x0)) + 1, 84 (int) Math.floor(x1)); // don't want to count mass below x0 85 } else { // x0 is mathematical integer, so use as is 86 return cumulativeProbability((int) Math.floor(x0), 87 (int) Math.floor(x1)); 88 } 89 } 90 91 /** 92 * For a random variable X whose values are distributed according 93 * to this distribution, this method returns P(X ≤ x). In other words, 94 * this method represents the probability distribution function, or PDF, 95 * for this distribution. 96 * 97 * @param x the value at which the PDF is evaluated. 98 * @return PDF for this distribution. 99 * @throws MathException if the cumulative probability can not be 100 * computed due to convergence or other numerical errors. 101 */ 102 abstract public double cumulativeProbability(int x) throws MathException; 103 104 /** 105 * For a random variable X whose values are distributed according 106 * to this distribution, this method returns P(X = x). In other words, this 107 * method represents the probability mass function, or PMF, for the distribution. 108 * <p> 109 * If <code>x</code> does not represent an integer value, 0 is returned. 110 * 111 * @param x the value at which the probability density function is evaluated 112 * @return the value of the probability density function at x 113 */ 114 public double probability(double x) { 115 double fl = Math.floor(x); 116 if (fl == x) { 117 return this.probability((int) x); 118 } else { 119 return 0; 120 } 121 } 122 123 /** 124 * For a random variable X whose values are distributed according 125 * to this distribution, this method returns P(x0 ≤ X ≤ x1). 126 * 127 * @param x0 the inclusive, lower bound 128 * @param x1 the inclusive, upper bound 129 * @return the cumulative probability. 130 * @throws MathException if the cumulative probability can not be 131 * computed due to convergence or other numerical errors. 132 * @throws IllegalArgumentException if x0 > x1 133 */ 134 public double cumulativeProbability(int x0, int x1) throws MathException { 135 if (x0 > x1) { 136 throw new IllegalArgumentException 137 ("lower endpoint must be less than or equal to upper endpoint"); 138 } 139 return cumulativeProbability(x1) - cumulativeProbability(x0 - 1); 140 } 141 142 /** 143 * For a random variable X whose values are distributed according 144 * to this distribution, this method returns the largest x, such 145 * that P(X ≤ x) ≤ <code>p</code>. 146 * 147 * @param p the desired probability 148 * @return the largest x such that P(X ≤ x) <= p 149 * @throws MathException if the inverse cumulative probability can not be 150 * computed due to convergence or other numerical errors. 151 * @throws IllegalArgumentException if p < 0 or p > 1 152 */ 153 public int inverseCumulativeProbability(final double p) throws MathException{ 154 if (p < 0.0 || p > 1.0) { 155 throw new IllegalArgumentException( 156 "p must be between 0 and 1.0 (inclusive)"); 157 } 158 159 // by default, do simple bisection. 160 // subclasses can override if there is a better method. 161 int x0 = getDomainLowerBound(p); 162 int x1 = getDomainUpperBound(p); 163 double pm; 164 while (x0 < x1) { 165 int xm = x0 + (x1 - x0) / 2; 166 pm = cumulativeProbability(xm); 167 if (pm > p) { 168 // update x1 169 if (xm == x1) { 170 // this can happen with integer division 171 // simply decrement x1 172 --x1; 173 } else { 174 // update x1 normally 175 x1 = xm; 176 } 177 } else { 178 // update x0 179 if (xm == x0) { 180 // this can happen with integer division 181 // simply increment x0 182 ++x0; 183 } else { 184 // update x0 normally 185 x0 = xm; 186 } 187 } 188 } 189 190 // insure x0 is the correct critical point 191 pm = cumulativeProbability(x0); 192 while (pm > p) { 193 --x0; 194 pm = cumulativeProbability(x0); 195 } 196 197 return x0; 198 } 199 200 /** 201 * Access the domain value lower bound, based on <code>p</code>, used to 202 * bracket a PDF root. This method is used by 203 * {@link #inverseCumulativeProbability(double)} to find critical values. 204 * 205 * @param p the desired probability for the critical value 206 * @return domain value lower bound, i.e. 207 * P(X < <i>lower bound</i>) < <code>p</code> 208 */ 209 protected abstract int getDomainLowerBound(double p); 210 211 /** 212 * Access the domain value upper bound, based on <code>p</code>, used to 213 * bracket a PDF root. This method is used by 214 * {@link #inverseCumulativeProbability(double)} to find critical values. 215 * 216 * @param p the desired probability for the critical value 217 * @return domain value upper bound, i.e. 218 * P(X < <i>upper bound</i>) > <code>p</code> 219 */ 220 protected abstract int getDomainUpperBound(double p); 221 }