1 /*
2 * Copyright 2003-2004 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 java.io.Serializable;
19
20 import org.apache.commons.math.ConvergenceException;
21 import org.apache.commons.math.FunctionEvaluationException;
22 import org.apache.commons.math.MathException;
23 import org.apache.commons.math.analysis.UnivariateRealFunction;
24 import org.apache.commons.math.analysis.UnivariateRealSolverUtils;
25
26 /**
27 * Base class for continuous distributions. Default implementations are
28 * provided for some of the methods that do not vary from distribution to
29 * distribution.
30 *
31 * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
32 */
33 public abstract class AbstractContinuousDistribution
34 extends AbstractDistribution
35 implements ContinuousDistribution, Serializable {
36
37 /** Serializable version identifier */
38 private static final long serialVersionUID = -38038050983108802L;
39
40 /**
41 * Default constructor.
42 */
43 protected AbstractContinuousDistribution() {
44 super();
45 }
46
47 /**
48 * For this distribution, X, this method returns the critical point x, such
49 * that P(X < x) = <code>p</code>.
50 *
51 * @param p the desired probability
52 * @return x, such that P(X < x) = <code>p</code>
53 * @throws MathException if the inverse cumulative probability can not be
54 * computed due to convergence or other numerical errors.
55 * @throws IllegalArgumentException if <code>p</code> is not a valid
56 * probability.
57 */
58 public double inverseCumulativeProbability(final double p)
59 throws MathException {
60 if (p < 0.0 || p > 1.0) {
61 throw new IllegalArgumentException("p must be between 0.0 and 1.0, inclusive.");
62 }
63
64 // by default, do simple root finding using bracketing and default solver.
65 // subclasses can overide if there is a better method.
66 UnivariateRealFunction rootFindingFunction =
67 new UnivariateRealFunction() {
68
69 public double value(double x) throws FunctionEvaluationException {
70 try {
71 return cumulativeProbability(x) - p;
72 } catch (MathException ex) {
73 throw new FunctionEvaluationException
74 (x, "Error computing cdf", ex);
75 }
76 }
77 };
78
79 // Try to bracket root, test domain endoints if this fails
80 double lowerBound = getDomainLowerBound(p);
81 double upperBound = getDomainUpperBound(p);
82 double[] bracket = null;
83 try {
84 bracket = UnivariateRealSolverUtils.bracket(
85 rootFindingFunction, getInitialDomain(p),
86 lowerBound, upperBound);
87 } catch (ConvergenceException ex) {
88 /*
89 * Check domain endpoints to see if one gives value that is within
90 * the default solver's defaultAbsoluteAccuracy of 0 (will be the
91 * case if density has bounded support and p is 0 or 1).
92 *
93 * TODO: expose the default solver, defaultAbsoluteAccuracy as
94 * a constant.
95 */
96 if (Math.abs(rootFindingFunction.value(lowerBound)) < 1E-6) {
97 return lowerBound;
98 }
99 if (Math.abs(rootFindingFunction.value(upperBound)) < 1E-6) {
100 return upperBound;
101 }
102 // Failed bracket convergence was not because of corner solution
103 throw new MathException(ex);
104 }
105
106 // find root
107 double root = UnivariateRealSolverUtils.solve(rootFindingFunction,
108 bracket[0],bracket[1]);
109 return root;
110 }
111
112 /**
113 * Access the initial domain value, based on <code>p</code>, used to
114 * bracket a CDF root. This method is used by
115 * {@link #inverseCumulativeProbability(double)} to find critical values.
116 *
117 * @param p the desired probability for the critical value
118 * @return initial domain value
119 */
120 protected abstract double getInitialDomain(double p);
121
122 /**
123 * Access the domain value lower bound, based on <code>p</code>, used to
124 * bracket a CDF root. This method is used by
125 * {@link #inverseCumulativeProbability(double)} to find critical values.
126 *
127 * @param p the desired probability for the critical value
128 * @return domain value lower bound, i.e.
129 * P(X < <i>lower bound</i>) < <code>p</code>
130 */
131 protected abstract double getDomainLowerBound(double p);
132
133 /**
134 * Access the domain value upper bound, based on <code>p</code>, used to
135 * bracket a CDF root. This method is used by
136 * {@link #inverseCumulativeProbability(double)} to find critical values.
137 *
138 * @param p the desired probability for the critical value
139 * @return domain value upper bound, i.e.
140 * P(X < <i>upper bound</i>) > <code>p</code>
141 */
142 protected abstract double getDomainUpperBound(double p);
143 }