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    }