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 }