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
18 package org.apache.commons.math.distribution;
19
20 import java.io.Serializable;
21
22 /**
23 * Default implementation of
24 * {@link org.apache.commons.math.distribution.CauchyDistribution}.
25 *
26 * @since 1.1
27 * @version $Revision: 617953 $ $Date: 2008-02-02 22:54:00 -0700 (Sat, 02 Feb 2008) $
28 */
29 public class CauchyDistributionImpl extends AbstractContinuousDistribution
30 implements CauchyDistribution, Serializable {
31
32 /** Serializable version identifier */
33 private static final long serialVersionUID = 8589540077390120676L;
34
35 /** The median of this distribution. */
36 private double median = 0;
37
38 /** The scale of this distribution. */
39 private double scale = 1;
40
41 /**
42 * Creates cauchy distribution with the medain equal to zero and scale
43 * equal to one.
44 */
45 public CauchyDistributionImpl(){
46 this(0.0, 1.0);
47 }
48
49 /**
50 * Create a cauchy distribution using the given median and scale.
51 * @param median median for this distribution
52 * @param s scale parameter for this distribution
53 */
54 public CauchyDistributionImpl(double median, double s){
55 super();
56 setMedian(median);
57 setScale(s);
58 }
59
60 /**
61 * For this disbution, X, this method returns P(X < <code>x</code>).
62 * @param x the value at which the CDF is evaluated.
63 * @return CDF evaluted at <code>x</code>.
64 */
65 public double cumulativeProbability(double x) {
66 return 0.5 + (Math.atan((x - median) / scale) / Math.PI);
67 }
68
69 /**
70 * Access the median.
71 * @return median for this distribution
72 */
73 public double getMedian() {
74 return median;
75 }
76
77 /**
78 * Access the scale parameter.
79 * @return scale parameter for this distribution
80 */
81 public double getScale() {
82 return scale;
83 }
84
85 /**
86 * For this distribution, X, this method returns the critical point x, such
87 * that P(X < x) = <code>p</code>.
88 * <p>
89 * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
90 * <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
91 *
92 * @param p the desired probability
93 * @return x, such that P(X < x) = <code>p</code>
94 * @throws IllegalArgumentException if <code>p</code> is not a valid
95 * probability.
96 */
97 public double inverseCumulativeProbability(double p) {
98 double ret;
99 if (p < 0.0 || p > 1.0) {
100 throw new IllegalArgumentException
101 ("probability argument must be between 0 and 1 (inclusive)");
102 } else if (p == 0) {
103 ret = Double.NEGATIVE_INFINITY;
104 } else if (p == 1) {
105 ret = Double.POSITIVE_INFINITY;
106 } else {
107 ret = median + scale * Math.tan(Math.PI * (p - .5));
108 }
109 return ret;
110 }
111
112 /**
113 * Modify the median.
114 * @param median for this distribution
115 */
116 public void setMedian(double median) {
117 this.median = median;
118 }
119
120 /**
121 * Modify the scale parameter.
122 * @param s scale parameter for this distribution
123 * @throws IllegalArgumentException if <code>sd</code> is not positive.
124 */
125 public void setScale(double s) {
126 if (s <= 0.0) {
127 throw new IllegalArgumentException(
128 "Scale must be positive.");
129 }
130 scale = s;
131 }
132
133 /**
134 * Access the domain value lower 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 lower bound, i.e.
140 * P(X < <i>lower bound</i>) < <code>p</code>
141 */
142 protected double getDomainLowerBound(double p) {
143 double ret;
144
145 if (p < .5) {
146 ret = -Double.MAX_VALUE;
147 } else {
148 ret = getMedian();
149 }
150
151 return ret;
152 }
153
154 /**
155 * Access the domain value upper bound, based on <code>p</code>, used to
156 * bracket a CDF root. This method is used by
157 * {@link #inverseCumulativeProbability(double)} to find critical values.
158 *
159 * @param p the desired probability for the critical value
160 * @return domain value upper bound, i.e.
161 * P(X < <i>upper bound</i>) > <code>p</code>
162 */
163 protected double getDomainUpperBound(double p) {
164 double ret;
165
166 if (p < .5) {
167 ret = getMedian();
168 } else {
169 ret = Double.MAX_VALUE;
170 }
171
172 return ret;
173 }
174
175 /**
176 * Access the initial domain value, based on <code>p</code>, used to
177 * bracket a CDF root. This method is used by
178 * {@link #inverseCumulativeProbability(double)} to find critical values.
179 *
180 * @param p the desired probability for the critical value
181 * @return initial domain value
182 */
183 protected double getInitialDomain(double p) {
184 double ret;
185
186 if (p < .5) {
187 ret = getMedian() - getScale();
188 } else if (p > .5) {
189 ret = getMedian() + getScale();
190 } else {
191 ret = getMedian();
192 }
193
194 return ret;
195 }
196 }