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 * https://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 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.distribution.continuous;
23
24 import org.hipparchus.exception.LocalizedCoreFormats;
25 import org.hipparchus.exception.MathIllegalArgumentException;
26 import org.hipparchus.util.FastMath;
27 import org.hipparchus.util.MathUtils;
28
29 /**
30 * Implementation of the Cauchy distribution.
31 *
32 * @see <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution (Wikipedia)</a>
33 * @see <a href="http://mathworld.wolfram.com/CauchyDistribution.html">Cauchy Distribution (MathWorld)</a>
34 */
35 public class CauchyDistribution extends AbstractRealDistribution {
36 /** Serializable version identifier */
37 private static final long serialVersionUID = 20160320L;
38 /** The median of this distribution. */
39 private final double median;
40 /** The scale of this distribution. */
41 private final double scale;
42
43 /**
44 * Creates a Cauchy distribution with the median equal to zero and scale
45 * equal to one.
46 */
47 public CauchyDistribution() {
48 this(0, 1);
49 }
50
51
52 /**
53 * Creates a Cauchy distribution.
54 *
55 * @param median Median for this distribution
56 * @param scale Scale parameter for this distribution
57 * @throws MathIllegalArgumentException if {@code scale <= 0}
58 */
59 public CauchyDistribution(double median, double scale)
60 throws MathIllegalArgumentException {
61 if (scale <= 0) {
62 throw new MathIllegalArgumentException(LocalizedCoreFormats.SCALE, scale);
63 }
64
65 this.scale = scale;
66 this.median = median;
67 }
68
69 /** {@inheritDoc} */
70 @Override
71 public double cumulativeProbability(double x) {
72 return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
73 }
74
75 /**
76 * Access the median.
77 *
78 * @return the median for this distribution.
79 */
80 public double getMedian() {
81 return median;
82 }
83
84 /**
85 * Access the scale parameter.
86 *
87 * @return the scale parameter for this distribution.
88 */
89 public double getScale() {
90 return scale;
91 }
92
93 /** {@inheritDoc} */
94 @Override
95 public double density(double x) {
96 final double dev = x - median;
97 return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
98 }
99
100 /**
101 * {@inheritDoc}
102 *
103 * Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
104 * and {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
105 */
106 @Override
107 public double inverseCumulativeProbability(double p) throws MathIllegalArgumentException {
108 MathUtils.checkRangeInclusive(p, 0, 1);
109
110 double ret;
111 if (p == 0) {
112 ret = Double.NEGATIVE_INFINITY;
113 } else if (p == 1) {
114 ret = Double.POSITIVE_INFINITY;
115 } else {
116 ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
117 }
118 return ret;
119 }
120
121 /**
122 * {@inheritDoc}
123 *
124 * The mean is always undefined no matter the parameters.
125 *
126 * @return mean (always Double.NaN)
127 */
128 @Override
129 public double getNumericalMean() {
130 return Double.NaN;
131 }
132
133 /**
134 * {@inheritDoc}
135 *
136 * The variance is always undefined no matter the parameters.
137 *
138 * @return variance (always Double.NaN)
139 */
140 @Override
141 public double getNumericalVariance() {
142 return Double.NaN;
143 }
144
145 /**
146 * {@inheritDoc}
147 *
148 * The lower bound of the support is always negative infinity no matter
149 * the parameters.
150 *
151 * @return lower bound of the support (always Double.NEGATIVE_INFINITY)
152 */
153 @Override
154 public double getSupportLowerBound() {
155 return Double.NEGATIVE_INFINITY;
156 }
157
158 /**
159 * {@inheritDoc}
160 *
161 * The upper bound of the support is always positive infinity no matter
162 * the parameters.
163 *
164 * @return upper bound of the support (always Double.POSITIVE_INFINITY)
165 */
166 @Override
167 public double getSupportUpperBound() {
168 return Double.POSITIVE_INFINITY;
169 }
170
171 /**
172 * {@inheritDoc}
173 *
174 * The support of this distribution is connected.
175 *
176 * @return {@code true}
177 */
178 @Override
179 public boolean isSupportConnected() {
180 return true;
181 }
182 }