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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.math.distribution;
18  
19  import org.apache.commons.math.MathException;
20  
21  /**
22   * Interface for discrete distributions of integer-valued random variables.
23   *
24   * @version $Revision: 670469 $ $Date: 2008-06-23 04:01:38 -0400 (Mon, 23 Jun 2008) $
25   */
26  public interface IntegerDistribution extends DiscreteDistribution {
27      /**
28       * For a random variable X whose values are distributed according
29       * to this distribution, this method returns P(X = x). In other words, this
30       * method represents the probability mass function for the distribution.
31       * 
32       * @param x the value at which the probability density function is evaluated.
33       * @return the value of the probability density function at x
34       */
35      double probability(int x);
36  
37      /**
38       * For a random variable X whose values are distributed according
39       * to this distribution, this method returns P(X ≤ x).  In other words,
40       * this method represents the probability distribution function, or PDF
41       * for the distribution.
42       * 
43       * @param x the value at which the PDF is evaluated.
44       * @return PDF for this distribution. 
45       * @throws MathException if the cumulative probability can not be
46       *            computed due to convergence or other numerical errors.
47       */
48      double cumulativeProbability(int x) throws MathException;
49      
50      /**
51       * For this distribution, X, this method returns P(x0 ≤ X ≤ x1).
52       * @param x0 the inclusive, lower bound
53       * @param x1 the inclusive, upper bound
54       * @return the cumulative probability. 
55       * @throws MathException if the cumulative probability can not be
56       *            computed due to convergence or other numerical errors.
57       * @throws IllegalArgumentException if x0 > x1
58       */
59      double cumulativeProbability(int x0, int x1) throws MathException;
60      
61      /**
62       * For this distribution, X, this method returns the largest x such that
63       * P(X &le; x) <= p.
64       * <p>
65       * Note that this definition implies: <ul>
66       * <li> If there is a minimum value, <code>m</code>, with postive
67       * probablility under (the density of) X, then <code>m - 1</code> is
68       * returned by <code>inverseCumulativeProbability(0).</code>  If there is
69       * no such value <code>m,  Integer.MIN_VALUE</code> is 
70       * returned.</li>
71       * <li> If there is a maximum value, <code>M</code>, such that
72       * P(X &le; M) =1, then <code>M</code> is returned by 
73       * <code>inverseCumulativeProbability(1).</code>
74       * If there is no such value, <code>M, Integer.MAX_VALUE</code> is 
75       * returned.</li></ul></p>
76       * 
77       * @param p the cumulative probability.
78       * @return the largest x such that P(X &le; x) <= p
79       * @throws MathException if the inverse cumulative probability can not be
80       *            computed due to convergence or other numerical errors.
81       * @throws IllegalArgumentException if p is not between 0 and 1 (inclusive)
82       */
83      int inverseCumulativeProbability(double p) throws MathException;
84  }