1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
|
package de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2013
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import de.lmu.ifi.dbs.elki.math.StatisticalMoments;
import de.lmu.ifi.dbs.elki.math.statistics.distribution.ExponentiallyModifiedGaussianDistribution;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Naive distribution estimation using mean and sample variance.
*
* @author Erich Schubert
*
* @apiviz.has ExponentiallyModifiedGaussianDistribution - - estimates
*/
@Reference(authors = "J. Olivier, M. M. Norberg", title = "Positively skewed data: Revisiting the Box-Cox power transformation", booktitle = "International Journal of Psychological Research Vol. 3 No. 1")
public class EMGOlivierNorbergEstimator extends AbstractMOMEstimator<ExponentiallyModifiedGaussianDistribution> {
/**
* Static estimator class.
*/
public static EMGOlivierNorbergEstimator STATIC = new EMGOlivierNorbergEstimator();
/**
* Private constructor, use static instance!
*/
private EMGOlivierNorbergEstimator() {
// Do not instantiate
}
@Override
public ExponentiallyModifiedGaussianDistribution estimateFromStatisticalMoments(StatisticalMoments moments) {
// Avoid NaN by disallowing negative kurtosis.
final double halfsk13 = Math.pow(Math.max(0., moments.getSampleSkewness() * .5), 1. / 3.);
final double st = moments.getSampleStddev();
final double mu = moments.getMean() - st * halfsk13;
// Note: we added "abs" here, to avoid even more NaNs.
final double si = st * Math.sqrt(Math.abs((1. + halfsk13) * (1. - halfsk13)));
// One more workaround to ensure finite lambda...
final double la = (halfsk13 > 0) ? 1 / (st * halfsk13) : 1;
return new ExponentiallyModifiedGaussianDistribution(mu, si, la);
}
@Override
public Class<? super ExponentiallyModifiedGaussianDistribution> getDistributionClass() {
return ExponentiallyModifiedGaussianDistribution.class;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected EMGOlivierNorbergEstimator makeInstance() {
return STATIC;
}
}
}
|
