    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.math.distribution;
    018
    019    import org.apache.commons.math.MathException;
    020
    021    /**
    022     * Interface for discrete distributions of integer-valued random variables.
    023     *
    024     * @version $Revision: 949535 $ $Date: 2010-05-30 19:00:15 +0200 (dim. 30 mai 2010) $
    025     */
    026    public interface IntegerDistribution extends DiscreteDistribution {
    027        /**
    028         * For a random variable X whose values are distributed according
    029         * to this distribution, this method returns P(X = x). In other words, this
    030         * method represents the probability mass function for the distribution.
    031         *
    032         * @param x the value at which the probability density function is evaluated.
    033         * @return the value of the probability density function at x
    034         */
    035        double probability(int x);
    036
    037        /**
    038         * For a random variable X whose values are distributed according
    039         * to this distribution, this method returns P(X &le; x).  In other words,
    040         * this method represents the probability distribution function, or PDF
    041         * for the distribution.
    042         *
    043         * @param x the value at which the PDF is evaluated.
    044         * @return PDF for this distribution.
    045         * @throws MathException if the cumulative probability can not be
    046         *            computed due to convergence or other numerical errors.
    047         */
    048        double cumulativeProbability(int x) throws MathException;
    049
    050        /**
    051         * For this distribution, X, this method returns P(x0 &le; X &le; x1).
    052         * @param x0 the inclusive, lower bound
    053         * @param x1 the inclusive, upper bound
    054         * @return the cumulative probability.
    055         * @throws MathException if the cumulative probability can not be
    056         *            computed due to convergence or other numerical errors.
    057         * @throws IllegalArgumentException if x0 > x1
    058         */
    059        double cumulativeProbability(int x0, int x1) throws MathException;
    060
    061        /**
    062         * For this distribution, X, this method returns the largest x such that
    063         * P(X &le; x) <= p.
    064         * <p>
    065         * Note that this definition implies: <ul>
    066         * <li> If there is a minimum value, <code>m</code>, with positive
    067         * probability under (the density of) X, then <code>m - 1</code> is
    068         * returned by <code>inverseCumulativeProbability(0).</code>  If there is
    069         * no such value <code>m,  Integer.MIN_VALUE</code> is
    070         * returned.</li>
    071         * <li> If there is a maximum value, <code>M</code>, such that
    072         * P(X &le; M) =1, then <code>M</code> is returned by
    073         * <code>inverseCumulativeProbability(1).</code>
    074         * If there is no such value, <code>M, Integer.MAX_VALUE</code> is
    075         * returned.</li></ul></p>
    076         *
    077         * @param p the cumulative probability.
    078         * @return the largest x such that P(X &le; x) <= p
    079         * @throws MathException if the inverse cumulative probability can not be
    080         *            computed due to convergence or other numerical errors.
    081         * @throws IllegalArgumentException if p is not between 0 and 1 (inclusive)
    082         */
    083        int inverseCumulativeProbability(double p) throws MathException;
    084    }