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.math3.distribution; 018 019 import org.apache.commons.math3.exception.NumberIsTooLargeException; 020 import org.apache.commons.math3.exception.OutOfRangeException; 021 022 /** 023 * Interface for distributions on the integers. 024 * 025 * @version $Id: IntegerDistribution.java 1416643 2012-12-03 19:37:14Z tn $ 026 */ 027 public interface IntegerDistribution { 028 /** 029 * For a random variable {@code X} whose values are distributed according 030 * to this distribution, this method returns {@code P(X = x)}. In other 031 * words, this method represents the probability mass function (PMF) 032 * for the distribution. 033 * 034 * @param x the point at which the PMF is evaluated 035 * @return the value of the probability mass function at {@code x} 036 */ 037 double probability(int x); 038 039 /** 040 * For a random variable {@code X} whose values are distributed according 041 * to this distribution, this method returns {@code P(X <= x)}. In other 042 * words, this method represents the (cumulative) distribution function 043 * (CDF) for this distribution. 044 * 045 * @param x the point at which the CDF is evaluated 046 * @return the probability that a random variable with this 047 * distribution takes a value less than or equal to {@code x} 048 */ 049 double cumulativeProbability(int x); 050 051 /** 052 * For a random variable {@code X} whose values are distributed according 053 * to this distribution, this method returns {@code P(x0 < X <= x1)}. 054 * 055 * @param x0 the exclusive lower bound 056 * @param x1 the inclusive upper bound 057 * @return the probability that a random variable with this distribution 058 * will take a value between {@code x0} and {@code x1}, 059 * excluding the lower and including the upper endpoint 060 * @throws NumberIsTooLargeException if {@code x0 > x1} 061 */ 062 double cumulativeProbability(int x0, int x1) throws NumberIsTooLargeException; 063 064 /** 065 * Computes the quantile function of this distribution. 066 * For a random variable {@code X} distributed according to this distribution, 067 * the returned value is 068 * <ul> 069 * <li><code>inf{x in Z | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li> 070 * <li><code>inf{x in Z | P(X<=x) > 0}</code> for {@code p = 0}.</li> 071 * </ul> 072 * If the result exceeds the range of the data type {@code int}, 073 * then {@code Integer.MIN_VALUE} or {@code Integer.MAX_VALUE} is returned. 074 * 075 * @param p the cumulative probability 076 * @return the smallest {@code p}-quantile of this distribution 077 * (largest 0-quantile for {@code p = 0}) 078 * @throws OutOfRangeException if {@code p < 0} or {@code p > 1} 079 */ 080 int inverseCumulativeProbability(double p) throws OutOfRangeException; 081 082 /** 083 * Use this method to get the numerical value of the mean of this 084 * distribution. 085 * 086 * @return the mean or {@code Double.NaN} if it is not defined 087 */ 088 double getNumericalMean(); 089 090 /** 091 * Use this method to get the numerical value of the variance of this 092 * distribution. 093 * 094 * @return the variance (possibly {@code Double.POSITIVE_INFINITY} or 095 * {@code Double.NaN} if it is not defined) 096 */ 097 double getNumericalVariance(); 098 099 /** 100 * Access the lower bound of the support. This method must return the same 101 * value as {@code inverseCumulativeProbability(0)}. In other words, this 102 * method must return 103 * <p><code>inf {x in Z | P(X <= x) > 0}</code>.</p> 104 * 105 * @return lower bound of the support ({@code Integer.MIN_VALUE} 106 * for negative infinity) 107 */ 108 int getSupportLowerBound(); 109 110 /** 111 * Access the upper bound of the support. This method must return the same 112 * value as {@code inverseCumulativeProbability(1)}. In other words, this 113 * method must return 114 * <p><code>inf {x in R | P(X <= x) = 1}</code>.</p> 115 * 116 * @return upper bound of the support ({@code Integer.MAX_VALUE} 117 * for positive infinity) 118 */ 119 int getSupportUpperBound(); 120 121 /** 122 * Use this method to get information about whether the support is 123 * connected, i.e. whether all integers between the lower and upper bound of 124 * the support are included in the support. 125 * 126 * @return whether the support is connected or not 127 */ 128 boolean isSupportConnected(); 129 130 /** 131 * Reseed the random generator used to generate samples. 132 * 133 * @param seed the new seed 134 * @since 3.0 135 */ 136 void reseedRandomGenerator(long seed); 137 138 /** 139 * Generate a random value sampled from this distribution. 140 * 141 * @return a random value 142 * @since 3.0 143 */ 144 int sample(); 145 146 /** 147 * Generate a random sample from the distribution. 148 * 149 * @param sampleSize the number of random values to generate 150 * @return an array representing the random sample 151 * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException 152 * if {@code sampleSize} is not positive 153 * @since 3.0 154 */ 155 int[] sample(int sampleSize); 156 }