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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) 2015
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.documentation.Reference;
/**
* Inner function of a kernel density estimator.
*
* Note: as of now, this API does not support asymmetric kernels.
*
* @author Erich Schubert
*/
public interface KernelDensityFunction {
/**
* Density contribution of a point at the given relative distance
* {@code delta >= 0}.
*
* Note that for {@code delta < 0}, in particular for {@code delta < 1}, the
* results may become invalid. So usually, you will want to invoke this as:
*
* {@code kernel.density(Math.abs(delta))}
*
* @param delta Relative distance
* @return density contribution
*/
public double density(double delta);
/**
* Get the canonical bandwidth for this kernel.
*
* Note: R uses a different definition of "canonical bandwidth", and also uses
* differently scaled kernels.
*
* @return Canonical bandwidth
*/
@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 double canonicalBandwidth();
/**
* Get the standard deviation of the kernel function.
*
* @return Standard deviation
*/
public double standardDeviation();
/**
* Get the R integral of the kernel, \int K^2(x) dx
*
* TODO: any better name for this?
*
* @return R value
*/
public double getR();
}
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