```001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
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 *
010 *
011 * Unless required by applicable law or agreed to in writing, software
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 */
017package org.apache.commons.math3.distribution;
018
019import org.apache.commons.math3.exception.NumberIsTooLargeException;
020import org.apache.commons.math3.exception.OutOfRangeException;
021
022/**
023 * Interface for distributions on the integers.
024 *
025 */
026public interface IntegerDistribution {
027    /**
028     * For a random variable {@code X} whose values are distributed according
029     * to this distribution, this method returns {@code P(X = x)}. In other
030     * words, this method represents the probability mass function (PMF)
031     * for the distribution.
032     *
033     * @param x the point at which the PMF is evaluated
034     * @return the value of the probability mass function at {@code x}
035     */
036    double probability(int x);
037
038    /**
039     * For a random variable {@code X} whose values are distributed according
040     * to this distribution, this method returns {@code P(X <= x)}.  In other
041     * words, this method represents the (cumulative) distribution function
042     * (CDF) for this distribution.
043     *
044     * @param x the point at which the CDF is evaluated
045     * @return the probability that a random variable with this
046     * distribution takes a value less than or equal to {@code x}
047     */
048    double cumulativeProbability(int x);
049
050    /**
051     * For a random variable {@code X} whose values are distributed according
052     * to this distribution, this method returns {@code P(x0 < X <= x1)}.
053     *
054     * @param x0 the exclusive lower bound
055     * @param x1 the inclusive upper bound
056     * @return the probability that a random variable with this distribution
057     * will take a value between {@code x0} and {@code x1},
058     * excluding the lower and including the upper endpoint
059     * @throws NumberIsTooLargeException if {@code x0 > x1}
060     */
061    double cumulativeProbability(int x0, int x1) throws NumberIsTooLargeException;
062
063    /**
064     * Computes the quantile function of this distribution.
065     * For a random variable {@code X} distributed according to this distribution,
066     * the returned value is
067     * <ul>
068     * <li><code>inf{x in Z | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li>
069     * <li><code>inf{x in Z | P(X<=x) > 0}</code> for {@code p = 0}.</li>
070     * </ul>
071     * If the result exceeds the range of the data type {@code int},
072     * then {@code Integer.MIN_VALUE} or {@code Integer.MAX_VALUE} is returned.
073     *
074     * @param p the cumulative probability
075     * @return the smallest {@code p}-quantile of this distribution
076     * (largest 0-quantile for {@code p = 0})
077     * @throws OutOfRangeException if {@code p < 0} or {@code p > 1}
078     */
079    int inverseCumulativeProbability(double p) throws OutOfRangeException;
080
081    /**
082     * Use this method to get the numerical value of the mean of this
083     * distribution.
084     *
085     * @return the mean or {@code Double.NaN} if it is not defined
086     */
087    double getNumericalMean();
088
089    /**
090     * Use this method to get the numerical value of the variance of this
091     * distribution.
092     *
093     * @return the variance (possibly {@code Double.POSITIVE_INFINITY} or
094     * {@code Double.NaN} if it is not defined)
095     */
096    double getNumericalVariance();
097
098    /**
099     * Access the lower bound of the support. This method must return the same
100     * value as {@code inverseCumulativeProbability(0)}. In other words, this
101     * method must return
102     * <p><code>inf {x in Z | P(X <= x) > 0}</code>.</p>
103     *
104     * @return lower bound of the support ({@code Integer.MIN_VALUE}
105     * for negative infinity)
106     */
107    int getSupportLowerBound();
108
109    /**
110     * Access the upper bound of the support. This method must return the same
111     * value as {@code inverseCumulativeProbability(1)}. In other words, this
112     * method must return
113     * <p><code>inf {x in R | P(X <= x) = 1}</code>.</p>
114     *
115     * @return upper bound of the support ({@code Integer.MAX_VALUE}
116     * for positive infinity)
117     */
118    int getSupportUpperBound();
119
120    /**
121     * Use this method to get information about whether the support is
122     * connected, i.e. whether all integers between the lower and upper bound of
123     * the support are included in the support.
124     *
125     * @return whether the support is connected or not
126     */
127    boolean isSupportConnected();
128
129    /**
130     * Reseed the random generator used to generate samples.
131     *
132     * @param seed the new seed
133     * @since 3.0
134     */
135    void reseedRandomGenerator(long seed);
136
137    /**
138     * Generate a random value sampled from this distribution.
139     *
140     * @return a random value
141     * @since 3.0
142     */
143    int sample();
144
145    /**
146     * Generate a random sample from the distribution.
147     *
148     * @param sampleSize the number of random values to generate
149     * @return an array representing the random sample
150     * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException
151     * if {@code sampleSize} is not positive
152     * @since 3.0
153     */
154    int[] sample(int sampleSize);
155}

```