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 * Base interface for distributions on the reals. 024 * 025 * @version $Id: RealDistribution.java 1416643 2012-12-03 19:37:14Z tn $ 026 * @since 3.0 027 */ 028 public interface RealDistribution { 029 /** 030 * For a random variable {@code X} whose values are distributed according 031 * to this distribution, this method returns {@code P(X = x)}. In other 032 * words, this method represents the probability mass function (PMF) 033 * for the distribution. 034 * 035 * @param x the point at which the PMF is evaluated 036 * @return the value of the probability mass function at point {@code x} 037 */ 038 double probability(double x); 039 040 /** 041 * Returns the probability density function (PDF) of this distribution 042 * evaluated at the specified point {@code x}. In general, the PDF is 043 * the derivative of the {@link #cumulativeProbability(double) CDF}. 044 * If the derivative does not exist at {@code x}, then an appropriate 045 * replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY}, 046 * {@code Double.NaN}, or the limit inferior or limit superior of the 047 * difference quotient. 048 * 049 * @param x the point at which the PDF is evaluated 050 * @return the value of the probability density function at point {@code x} 051 */ 052 double density(double x); 053 054 /** 055 * For a random variable {@code X} whose values are distributed according 056 * to this distribution, this method returns {@code P(X <= x)}. In other 057 * words, this method represents the (cumulative) distribution function 058 * (CDF) for this distribution. 059 * 060 * @param x the point at which the CDF is evaluated 061 * @return the probability that a random variable with this 062 * distribution takes a value less than or equal to {@code x} 063 */ 064 double cumulativeProbability(double x); 065 066 /** 067 * For a random variable {@code X} whose values are distributed according 068 * to this distribution, this method returns {@code P(x0 < X <= x1)}. 069 * 070 * @param x0 the exclusive lower bound 071 * @param x1 the inclusive upper bound 072 * @return the probability that a random variable with this distribution 073 * takes a value between {@code x0} and {@code x1}, 074 * excluding the lower and including the upper endpoint 075 * @throws NumberIsTooLargeException if {@code x0 > x1} 076 * 077 * @deprecated As of 3.1. In 4.0, this method will be renamed 078 * {@code probability(double x0, double x1)}. 079 */ 080 @Deprecated 081 double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException; 082 083 /** 084 * Computes the quantile function of this distribution. For a random 085 * variable {@code X} distributed according to this distribution, the 086 * returned value is 087 * <ul> 088 * <li><code>inf{x in R | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li> 089 * <li><code>inf{x in R | P(X<=x) > 0}</code> for {@code p = 0}.</li> 090 * </ul> 091 * 092 * @param p the cumulative probability 093 * @return the smallest {@code p}-quantile of this distribution 094 * (largest 0-quantile for {@code p = 0}) 095 * @throws OutOfRangeException if {@code p < 0} or {@code p > 1} 096 */ 097 double inverseCumulativeProbability(double p) throws OutOfRangeException; 098 099 /** 100 * Use this method to get the numerical value of the mean of this 101 * distribution. 102 * 103 * @return the mean or {@code Double.NaN} if it is not defined 104 */ 105 double getNumericalMean(); 106 107 /** 108 * Use this method to get the numerical value of the variance of this 109 * distribution. 110 * 111 * @return the variance (possibly {@code Double.POSITIVE_INFINITY} as 112 * for certain cases in {@link TDistribution}) or {@code Double.NaN} if it 113 * is not defined 114 */ 115 double getNumericalVariance(); 116 117 /** 118 * Access the lower bound of the support. This method must return the same 119 * value as {@code inverseCumulativeProbability(0)}. In other words, this 120 * method must return 121 * <p><code>inf {x in R | P(X <= x) > 0}</code>.</p> 122 * 123 * @return lower bound of the support (might be 124 * {@code Double.NEGATIVE_INFINITY}) 125 */ 126 double getSupportLowerBound(); 127 128 /** 129 * Access the upper bound of the support. This method must return the same 130 * value as {@code inverseCumulativeProbability(1)}. In other words, this 131 * method must return 132 * <p><code>inf {x in R | P(X <= x) = 1}</code>.</p> 133 * 134 * @return upper bound of the support (might be 135 * {@code Double.POSITIVE_INFINITY}) 136 */ 137 double getSupportUpperBound(); 138 139 /** 140 * Whether or not the lower bound of support is in the domain of the density 141 * function. Returns true iff {@code getSupporLowerBound()} is finite and 142 * {@code density(getSupportLowerBound())} returns a non-NaN, non-infinite 143 * value. 144 * 145 * @return true if the lower bound of support is finite and the density 146 * function returns a non-NaN, non-infinite value there 147 * @deprecated to be removed in 4.0 148 */ 149 boolean isSupportLowerBoundInclusive(); 150 151 /** 152 * Whether or not the upper bound of support is in the domain of the density 153 * function. Returns true iff {@code getSupportUpperBound()} is finite and 154 * {@code density(getSupportUpperBound())} returns a non-NaN, non-infinite 155 * value. 156 * 157 * @return true if the upper bound of support is finite and the density 158 * function returns a non-NaN, non-infinite value there 159 * @deprecated to be removed in 4.0 160 */ 161 boolean isSupportUpperBoundInclusive(); 162 163 /** 164 * Use this method to get information about whether the support is connected, 165 * i.e. whether all values between the lower and upper bound of the support 166 * are included in the support. 167 * 168 * @return whether the support is connected or not 169 */ 170 boolean isSupportConnected(); 171 172 /** 173 * Reseed the random generator used to generate samples. 174 * 175 * @param seed the new seed 176 */ 177 void reseedRandomGenerator(long seed); 178 179 /** 180 * Generate a random value sampled from this distribution. 181 * 182 * @return a random value. 183 */ 184 double sample(); 185 186 /** 187 * Generate a random sample from the distribution. 188 * 189 * @param sampleSize the number of random values to generate 190 * @return an array representing the random sample 191 * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException 192 * if {@code sampleSize} is not positive 193 */ 194 double[] sample(int sampleSize); 195 }