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Java > Open Source Codes > org > apache > commons > math > distribution > IntegerDistribution


1 /*
2  * Copyright 2004 The Apache Software Foundation.
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  * http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 package org.apache.commons.math.distribution;
17
18 import org.apache.commons.math.MathException;
19
20 /**
21  * Interface for discrete distributions of integer-valued random variables.
22  *
23  * @version $Revision$ $Date: 2005-02-26 05:11:52 -0800 (Sat, 26 Feb 2005) $
24  */
25 public interface IntegerDistribution extends DiscreteDistribution {
26     /**
27      * For a random variable X whose values are distributed according
28      * to this distribution, this method returns P(X = x). In other words, this
29      * method represents the probability mass function for the distribution.
30      *
31      * @param x the value at which the probability density function is evaluated.
32      * @return the value of the probability density function at x
33      */
34     double probability(int x);
35
36     /**
37      * For a random variable X whose values are distributed according
38      * to this distribution, this method returns P(X ≤ x). In other words,
39      * this method represents the probability distribution function, or PDF
40      * for the distribution.
41      *
42      * @param x the value at which the PDF is evaluated.
43      * @return PDF for this distribution.
44      * @throws MathException if the cumulative probability can not be
45      * computed due to convergence or other numerical errors.
46      */
47     double cumulativeProbability(int x) throws MathException;
48     
49     /**
50      * For this distribution, X, this method returns P(x0 ≤ X ≤ x1).
51      * @param x0 the inclusive, lower bound
52      * @param x1 the inclusive, upper bound
53      * @return the cumulative probability.
54      * @throws MathException if the cumulative probability can not be
55      * computed due to convergence or other numerical errors.
56      * @throws IllegalArgumentException if x0 > x1
57      */
58     double cumulativeProbability(int x0, int x1) throws MathException;
59     
60     /**
61      * For this distribution, X, this method returns the largest x such that
62      * P(X &le; x) <= p.
63      * <p>
64      * Note that this definition implies: <ul>
65      * <li> If there is a minimum value, <code>m</code>, with postive
66      * probablility under (the density of) X, then <code>m - 1</code> is
67      * returned by <code>inverseCumulativeProbability(0).</code> If there is
68      * no such value <code>m, Integer.MIN_VALUE</code> is
69      * returned.</li>
70      * <li> If there is a maximum value, <code>M</code>, such that
71      * P(X &le; M) =1, then <code>M</code> is returned by
72      * <code>inverseCumulativeProbability(1).</code>
73      * If there is no such value, <code>M, Integer.MAX_VALUE</code> is
74      * returned.</li></ul>
75      *
76      * @param p the cumulative probability.
77      * @return the largest x such that P(X &le; x) <= p
78      * @throws MathException if the inverse cumulative probability can not be
79      * computed due to convergence or other numerical errors.
80      * @throws IllegalArgumentException if p is not between 0 and 1 (inclusive)
81      */
82     int inverseCumulativeProbability(double p) throws MathException;
83 }
84
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