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 org.apache.commons.math.MathException; 20 21 /** 22 * Interface for discrete distributions of integer-valued random variables. 23 * 24 * @version $Revision: 949535 $ $Date: 2010-05-30 19:00:15 +0200 (dim. 30 mai 2010) $ 25 */ 26 public interface IntegerDistribution extends DiscreteDistribution { 27 /** 28 * For a random variable X whose values are distributed according 29 * to this distribution, this method returns P(X = x). In other words, this 30 * method represents the probability mass function for the distribution. 31 * 32 * @param x the value at which the probability density function is evaluated. 33 * @return the value of the probability density function at x 34 */ 35 double probability(int x); 36 37 /** 38 * For a random variable X whose values are distributed according 39 * to this distribution, this method returns P(X ≤ x). In other words, 40 * this method represents the probability distribution function, or PDF 41 * for the distribution. 42 * 43 * @param x the value at which the PDF is evaluated. 44 * @return PDF for this distribution. 45 * @throws MathException if the cumulative probability can not be 46 * computed due to convergence or other numerical errors. 47 */ 48 double cumulativeProbability(int x) throws MathException; 49 50 /** 51 * For this distribution, X, this method returns P(x0 ≤ X ≤ x1). 52 * @param x0 the inclusive, lower bound 53 * @param x1 the inclusive, upper bound 54 * @return the cumulative probability. 55 * @throws MathException if the cumulative probability can not be 56 * computed due to convergence or other numerical errors. 57 * @throws IllegalArgumentException if x0 > x1 58 */ 59 double cumulativeProbability(int x0, int x1) throws MathException; 60 61 /** 62 * For this distribution, X, this method returns the largest x such that 63 * P(X ≤ x) <= p. 64 * <p> 65 * Note that this definition implies: <ul> 66 * <li> If there is a minimum value, <code>m</code>, with positive 67 * probability under (the density of) X, then <code>m - 1</code> is 68 * returned by <code>inverseCumulativeProbability(0).</code> If there is 69 * no such value <code>m, Integer.MIN_VALUE</code> is 70 * returned.</li> 71 * <li> If there is a maximum value, <code>M</code>, such that 72 * P(X ≤ M) =1, then <code>M</code> is returned by 73 * <code>inverseCumulativeProbability(1).</code> 74 * If there is no such value, <code>M, Integer.MAX_VALUE</code> is 75 * returned.</li></ul></p> 76 * 77 * @param p the cumulative probability. 78 * @return the largest x such that P(X ≤ x) <= p 79 * @throws MathException if the inverse cumulative probability can not be 80 * computed due to convergence or other numerical errors. 81 * @throws IllegalArgumentException if p is not between 0 and 1 (inclusive) 82 */ 83 int inverseCumulativeProbability(double p) throws MathException; 84 } 85
