1 /*
2  * This file is part of ELKI:
3  * Environment for Developing KDD-Applications Supported by Index-Structures
4  *
5  * Copyright (C) 2018
6  * ELKI Development Team
7  *
8  * This program is free software: you can redistribute it and/or modify
9  * it under the terms of the GNU Affero General Public License as published by
10  * the Free Software Foundation, either version 3 of the License, or
11  * (at your option) any later version.
12  *
13  * This program is distributed in the hope that it will be useful,
14  * but WITHOUT ANY WARRANTY; without even the implied warranty of
15  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16  * GNU Affero General Public License for more details.
17  *
18  * You should have received a copy of the GNU Affero General Public License
19  * along with this program. If not, see <http://www.gnu.org/licenses/>.
20  */
21 package de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator;
22 
23 import de.lmu.ifi.dbs.elki.math.MathUtil;
24 import de.lmu.ifi.dbs.elki.math.statistics.distribution.NormalDistribution;
25 import de.lmu.ifi.dbs.elki.math.statistics.distribution.SkewGeneralizedNormalDistribution;
26 import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
27 import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
28 import net.jafama.FastMath;
29 
30 /**
31  * Estimate the parameters of a skew Normal Distribution (Hoskin's Generalized
32  * Normal Distribution), using the methods of L-Moments (LMM).
33  * <p>
34  * Reference:
35  * <p>
36  * J. R. M. Hosking<br>
37  * Fortran routines for use with the method of L-moments Version 3.03<br>
38  * IBM Research.
39  *
40  * @author Erich Schubert
41  * @since 0.6.0
42  *
43  * @has - - - SkewGeneralizedNormalDistribution
44  */
45 @Reference(authors = "J. R. M. Hosking", //
46     title = "Fortran routines for use with the method of L-moments Version 3.03", //
47     booktitle = "IBM Research Technical Report", //
48     bibkey = "tr/ibm/Hosking00")
49 public class SkewGNormalLMMEstimator implements LMMDistributionEstimator<SkewGeneralizedNormalDistribution> {
50   /**
51    * Static instance.
52    */
53   public static final SkewGNormalLMMEstimator STATIC = new SkewGNormalLMMEstimator();
54 
55   /** Polynomial approximation */
56   private static final double //
57   A0 = 0.20466534e+01, //
58       A1 = -0.36544371e+01, //
59       A2 = 0.18396733e+01, //
60       A3 = -0.20360244;
61 
62   /** Polynomial approximation */
63   private static final double //
64   B1 = -0.20182173e+01, //
65       B2 = 0.12420401e+01, //
66       B3 = -0.21741801;
67 
68   /**
69    * Constructor. Private: use static instance.
70    */
SkewGNormalLMMEstimator()71   private SkewGNormalLMMEstimator() {
72     super();
73   }
74 
75   @Override
getNumMoments()76   public int getNumMoments() {
77     return 3;
78   }
79 
80   @Override
estimateFromLMoments(double[] xmom)81   public SkewGeneralizedNormalDistribution estimateFromLMoments(double[] xmom) {
82     if(!(xmom[1] > 0.) || !(Math.abs(xmom[2]) < 1.0)) {
83       throw new ArithmeticException("L-Moments invalid");
84     }
85     // Generalized Normal Distribution estimation:
86     double t3 = xmom[2];
87     if(Math.abs(t3) >= .95) {
88       // Extreme skewness
89       return new SkewGeneralizedNormalDistribution(0., -1., 0.);
90     }
91     if(Math.abs(t3) <= 1e-8) {
92       // t3 effectively zero, this is a normal distribution.
93       return new SkewGeneralizedNormalDistribution(xmom[0], xmom[1] * MathUtil.SQRTPI, 0.);
94     }
95     final double tt = t3 * t3;
96     double shape = -t3 * (A0 + tt * (A1 + tt * (A2 + tt * A3))) / (1. + tt * (B1 + tt * (B2 + tt * B3)));
97     final double e = FastMath.exp(.5 * shape * shape);
98     double scale = xmom[1] * shape / (e * NormalDistribution.erf(.5 * shape));
99     double location = xmom[0] + scale * (e - 1.) / shape;
100     return new SkewGeneralizedNormalDistribution(location, scale, shape);
101   }
102 
103   @Override
getDistributionClass()104   public Class<? super SkewGeneralizedNormalDistribution> getDistributionClass() {
105     return SkewGeneralizedNormalDistribution.class;
106   }
107 
108   @Override
toString()109   public String toString() {
110     return this.getClass().getSimpleName();
111   }
112 
113   /**
114    * Parameterization class.
115    *
116    * @author Erich Schubert
117    */
118   public static class Parameterizer extends AbstractParameterizer {
119     @Override
makeInstance()120     protected SkewGNormalLMMEstimator makeInstance() {
121       return STATIC;
122     }
123   }
124 }
125