1 /* 2 * Copyright 2003-2004 The Apache Software Foundation. 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 package org.apache.commons.math.distribution; 17 18 import java.io.Serializable; 19 20 import org.apache.commons.math.MathException; 21 22 23 /** 24 * Base class for integer-valued discrete distributions. Default 25 * implementations are provided for some of the methods that do not vary 26 * from distribution to distribution. 27 * 28 * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $ 29 */ 30 public abstract class AbstractIntegerDistribution extends AbstractDistribution 31 implements IntegerDistribution, Serializable { 32 33 /** Serializable version identifier */ 34 private static final long serialVersionUID = -1146319659338487221L; 35 36 /** 37 * Default constructor. 38 */ 39 protected AbstractIntegerDistribution() { 40 super(); 41 } 42 43 /** 44 * For a random variable X whose values are distributed according 45 * to this distribution, this method returns P(X ≤ x). In other words, 46 * this method represents the (cumulative) distribution function, or 47 * CDF, for this distribution. 48 * <p> 49 * If <code>x</code> does not represent an integer value, the CDF is 50 * evaluated at the greatest integer less than x. 51 * 52 * @param x the value at which the distribution function is evaluated. 53 * @return cumulative probability that a random variable with this 54 * distribution takes a value less than or equal to <code>x</code> 55 * @throws MathException if the cumulative probability can not be 56 * computed due to convergence or other numerical errors. 57 */ 58 public double cumulativeProbability(double x) throws MathException { 59 return cumulativeProbability((int) Math.floor(x)); 60 } 61 62 /** 63 * For a random variable X whose values are distributed according 64 * to this distribution, this method returns P(X ≤ x). In other words, 65 * this method represents the probability distribution function, or PDF, 66 * for this distribution. 67 * 68 * @param x the value at which the PDF is evaluated. 69 * @return PDF for this distribution. 70 * @throws MathException if the cumulative probability can not be 71 * computed due to convergence or other numerical errors. 72 */ 73 abstract public double cumulativeProbability(int x) throws MathException; 74 75 /** 76 * For a random variable X whose values are distributed according 77 * to this distribution, this method returns P(X = x). In other words, this 78 * method represents the probability mass function, or PMF, for the distribution. 79 * <p> 80 * If <code>x</code> does not represent an integer value, 0 is returned. 81 * 82 * @param x the value at which the probability density function is evaluated 83 * @return the value of the probability density function at x 84 */ 85 public double probability(double x) { 86 double fl = Math.floor(x); 87 if (fl == x) { 88 return this.probability((int) x); 89 } else { 90 return 0; 91 } 92 } 93 94 /** 95 * For a random variable X whose values are distributed according 96 * to this distribution, this method returns P(x0 ≤ X ≤ x1). 97 * 98 * @param x0 the inclusive, lower bound 99 * @param x1 the inclusive, upper bound 100 * @return the cumulative probability. 101 * @throws MathException if the cumulative probability can not be 102 * computed due to convergence or other numerical errors. 103 * @throws IllegalArgumentException if x0 > x1 104 */ 105 public double cumulativeProbability(int x0, int x1) throws MathException { 106 if (x0 > x1) { 107 throw new IllegalArgumentException 108 ("lower endpoint must be less than or equal to upper endpoint"); 109 } 110 return cumulativeProbability(x1) - cumulativeProbability(x0 - 1); 111 } 112 113 /** 114 * For a random variable X whose values are distributed according 115 * to this distribution, this method returns the largest x, such 116 * that P(X ≤ x) ≤ <code>p</code>. 117 * 118 * @param p the desired probability 119 * @return the largest x such that P(X ≤ x) <= p 120 * @throws MathException if the inverse cumulative probability can not be 121 * computed due to convergence or other numerical errors. 122 * @throws IllegalArgumentException if p < 0 or p > 1 123 */ 124 public int inverseCumulativeProbability(final double p) throws MathException{ 125 if (p < 0.0 || p > 1.0) { 126 throw new IllegalArgumentException( 127 "p must be between 0 and 1.0 (inclusive)"); 128 } 129 130 // by default, do simple bisection. 131 // subclasses can override if there is a better method. 132 int x0 = getDomainLowerBound(p); 133 int x1 = getDomainUpperBound(p); 134 double pm; 135 while (x0 < x1) { 136 int xm = x0 + (x1 - x0) / 2; 137 pm = cumulativeProbability(xm); 138 if (pm > p) { 139 // update x1 140 if (xm == x1) { 141 // this can happen with integer division 142 // simply decrement x1 143 --x1; 144 } else { 145 // update x1 normally 146 x1 = xm; 147 } 148 } else { 149 // update x0 150 if (xm == x0) { 151 // this can happen with integer division 152 // simply increment x0 153 ++x0; 154 } else { 155 // update x0 normally 156 x0 = xm; 157 } 158 } 159 } 160 161 // insure x0 is the correct critical point 162 pm = cumulativeProbability(x0); 163 while (pm > p) { 164 --x0; 165 pm = cumulativeProbability(x0); 166 } 167 168 return x0; 169 } 170 171 /** 172 * Access the domain value lower bound, based on <code>p</code>, used to 173 * bracket a PDF root. This method is used by 174 * {@link #inverseCumulativeProbability(double)} to find critical values. 175 * 176 * @param p the desired probability for the critical value 177 * @return domain value lower bound, i.e. 178 * P(X < <i>lower bound</i>) < <code>p</code> 179 */ 180 protected abstract int getDomainLowerBound(double p); 181 182 /** 183 * Access the domain value upper bound, based on <code>p</code>, used to 184 * bracket a PDF root. This method is used by 185 * {@link #inverseCumulativeProbability(double)} to find critical values. 186 * 187 * @param p the desired probability for the critical value 188 * @return domain value upper bound, i.e. 189 * P(X < <i>upper bound</i>) > <code>p</code> 190 */ 191 protected abstract int getDomainUpperBound(double p); 192 }