de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions

Interface KernelDensityFunction

All Known Implementing Classes:

BiweightKernelDensityFunction, CosineKernelDensityFunction, EpanechnikovKernelDensityFunction, GaussianKernelDensityFunction, TriangularKernelDensityFunction, TricubeKernelDensityFunction, TriweightKernelDensityFunction, UniformKernelDensityFunction

public interface KernelDensityFunction

Inner function of a kernel density estimator.

Note: as of now, this API does not support asymmetric kernels, which would be difficult in the multivariate case.

Since:

0.6.0

Author:

Erich Schubert

Method Summary

Modifier and Type	Method and Description
double	canonicalBandwidth() Get the canonical bandwidth for this kernel.
double	density(double delta) Density contribution of a point at the given relative distance delta >= 0.
double	getR() Get the R integral of the kernel, \int K^2(x) dx TODO: any better name for this?
double	standardDeviation() Get the standard deviation of the kernel function.

Method Detail

density

double density(double delta)

Density contribution of a point at the given relative distance delta >= 0.

Note that for delta < 0, in particular for delta < 1, the results may become invalid. So usually, you will want to invoke this as:

kernel.density(Math.abs(delta))

Parameters:

delta - Relative distance

Returns:

density contribution

canonicalBandwidth

@Reference(authors="J. S. Marron, D. Nolan",
           title="Canonical kernels for density estimation",
           booktitle="Statistics & Probability Letters, Volume 7, Issue 3",
           url="https://doi.org/10.1016/0167-7152(88)90050-8",
           bibkey="doi:10.1016/0167-71528890050-8")
double canonicalBandwidth()

Get the canonical bandwidth for this kernel.

Note: R uses a different definition of "canonical bandwidth", and also uses differently scaled kernels.

Returns:

Canonical bandwidth

standardDeviation

double standardDeviation()

Get the standard deviation of the kernel function.

Returns:

Standard deviation

getR

double getR()

Get the R integral of the kernel, \int K^2(x) dx

TODO: any better name for this?

Returns:

R value