001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.distribution;
019
020 import java.io.Serializable;
021
022 /**
023 * Default implementation of
024 * {@link org.apache.commons.math.distribution.CauchyDistribution}.
025 *
026 * @since 1.1
027 * @version $Revision: 670469 $ $Date: 2008-06-23 10:01:38 +0200 (lun, 23 jun 2008) $
028 */
029 public class CauchyDistributionImpl extends AbstractContinuousDistribution
030 implements CauchyDistribution, Serializable {
031
032 /** Serializable version identifier */
033 private static final long serialVersionUID = 8589540077390120676L;
034
035 /** The median of this distribution. */
036 private double median = 0;
037
038 /** The scale of this distribution. */
039 private double scale = 1;
040
041 /**
042 * Creates cauchy distribution with the medain equal to zero and scale
043 * equal to one.
044 */
045 public CauchyDistributionImpl(){
046 this(0.0, 1.0);
047 }
048
049 /**
050 * Create a cauchy distribution using the given median and scale.
051 * @param median median for this distribution
052 * @param s scale parameter for this distribution
053 */
054 public CauchyDistributionImpl(double median, double s){
055 super();
056 setMedian(median);
057 setScale(s);
058 }
059
060 /**
061 * For this distribution, X, this method returns P(X < <code>x</code>).
062 * @param x the value at which the CDF is evaluated.
063 * @return CDF evaluted at <code>x</code>.
064 */
065 public double cumulativeProbability(double x) {
066 return 0.5 + (Math.atan((x - median) / scale) / Math.PI);
067 }
068
069 /**
070 * Access the median.
071 * @return median for this distribution
072 */
073 public double getMedian() {
074 return median;
075 }
076
077 /**
078 * Access the scale parameter.
079 * @return scale parameter for this distribution
080 */
081 public double getScale() {
082 return scale;
083 }
084
085 /**
086 * For this distribution, X, this method returns the critical point x, such
087 * that P(X < x) = <code>p</code>.
088 * <p>
089 * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
090 * <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
091 *
092 * @param p the desired probability
093 * @return x, such that P(X < x) = <code>p</code>
094 * @throws IllegalArgumentException if <code>p</code> is not a valid
095 * probability.
096 */
097 public double inverseCumulativeProbability(double p) {
098 double ret;
099 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 }