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package de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions;
/*
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.utilities.Alias;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Epanechnikov kernel density estimator.
*
* @author Erich Schubert
*/
@Alias({ "epanechnikov" })
public final class EpanechnikovKernelDensityFunction implements KernelDensityFunction {
/**
* Static instance.
*/
public static final EpanechnikovKernelDensityFunction KERNEL = new EpanechnikovKernelDensityFunction();
/**
* Canonical bandwidth: 15^(1/5)
*/
@Reference(authors = "J.S. Marron, D. Nolan", title = "Canonical kernels for density estimation", booktitle = "Statistics & Probability Letters, Volume 7, Issue 3", url = "http://dx.doi.org/10.1016/0167-7152(88)90050-8")
public static final double CANONICAL_BANDWIDTH = Math.pow(15., .2);
/**
* Standard deviation.
*/
public static final double STDDEV = 1. / Math.sqrt(5.);
/**
* R constant.
*/
public static final double R = 3. / 5.;
/**
* Private, empty constructor. Use the static instance!
*/
private EpanechnikovKernelDensityFunction() {
// Nothing to do.
}
@Override
public double density(double delta) {
return (delta < 1.) ? .75 * (1 - delta * delta) : 0.;
}
@Override
public double canonicalBandwidth() {
return CANONICAL_BANDWIDTH;
}
@Override
public double standardDeviation() {
return STDDEV;
}
@Override
public double getR() {
return R;
}
/**
* Parameterization stub.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected EpanechnikovKernelDensityFunction makeInstance() {
return KERNEL;
}
}
}
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