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: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
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 ≤ 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 ≤ X ≤ 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 postive
067         * probablility 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    }