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: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 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 ≤ 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 ≤ 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 ≤ 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 }