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.special.Gamma;
27 import org.hipparchus.util.FastMath;
28
29 /**
30 * This class implements the Nakagami distribution.
31 *
32 * @see <a href="http://en.wikipedia.org/wiki/Nakagami_distribution">Nakagami Distribution (Wikipedia)</a>
33 */
34 public class NakagamiDistribution extends AbstractRealDistribution {
35
36 /** Serializable version identifier. */
37 private static final long serialVersionUID = 20141003;
38
39 /** The shape parameter. */
40 private final double mu;
41 /** The scale parameter. */
42 private final double omega;
43
44 /**
45 * Build a new instance.
46 *
47 * @param mu shape parameter
48 * @param omega scale parameter (must be positive)
49 * @throws MathIllegalArgumentException if {@code mu < 0.5}
50 * @throws MathIllegalArgumentException if {@code omega <= 0}
51 */
52 public NakagamiDistribution(double mu, double omega)
53 throws MathIllegalArgumentException {
54 this(mu, omega, DEFAULT_SOLVER_ABSOLUTE_ACCURACY);
55 }
56
57 /**
58 * Build a new instance.
59 *
60 * @param mu shape parameter
61 * @param omega scale parameter (must be positive)
62 * @param inverseAbsoluteAccuracy the maximum absolute error in inverse
63 * cumulative probability estimates (defaults to {@link #DEFAULT_SOLVER_ABSOLUTE_ACCURACY}).
64 * @throws MathIllegalArgumentException if {@code mu < 0.5}
65 * @throws MathIllegalArgumentException if {@code omega <= 0}
66 */
67 public NakagamiDistribution(double mu,
68 double omega,
69 double inverseAbsoluteAccuracy)
70 throws MathIllegalArgumentException {
71 super(inverseAbsoluteAccuracy);
72
73 if (mu < 0.5) {
74 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
75 mu, 0.5);
76 }
77 if (omega <= 0) {
78 throw new MathIllegalArgumentException(LocalizedCoreFormats.NOT_POSITIVE_SCALE, omega);
79 }
80
81 this.mu = mu;
82 this.omega = omega;
83 }
84
85 /**
86 * Access the shape parameter, {@code mu}.
87 *
88 * @return the shape parameter.
89 */
90 public double getShape() {
91 return mu;
92 }
93
94 /**
95 * Access the scale parameter, {@code omega}.
96 *
97 * @return the scale parameter.
98 */
99 public double getScale() {
100 return omega;
101 }
102
103 /** {@inheritDoc} */
104 @Override
105 public double density(double x) {
106 if (x <= 0) {
107 return 0.0;
108 }
109 return 2.0 * FastMath.pow(mu, mu) / (Gamma.gamma(mu) * FastMath.pow(omega, mu)) *
110 FastMath.pow(x, 2 * mu - 1) * FastMath.exp(-mu * x * x / omega);
111 }
112
113 /** {@inheritDoc} */
114 @Override
115 public double cumulativeProbability(double x) {
116 return Gamma.regularizedGammaP(mu, mu * x * x / omega);
117 }
118
119 /** {@inheritDoc} */
120 @Override
121 public double getNumericalMean() {
122 return Gamma.gamma(mu + 0.5) / Gamma.gamma(mu) * FastMath.sqrt(omega / mu);
123 }
124
125 /** {@inheritDoc} */
126 @Override
127 public double getNumericalVariance() {
128 double v = Gamma.gamma(mu + 0.5) / Gamma.gamma(mu);
129 return omega * (1 - 1 / mu * v * v);
130 }
131
132 /** {@inheritDoc} */
133 @Override
134 public double getSupportLowerBound() {
135 return 0;
136 }
137
138 /** {@inheritDoc} */
139 @Override
140 public double getSupportUpperBound() {
141 return Double.POSITIVE_INFINITY;
142 }
143
144 /** {@inheritDoc} */
145 @Override
146 public boolean isSupportConnected() {
147 return true;
148 }
149
150 }