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.

Method Summary

Methods

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="http://dx.doi.org/10.1016/0167-7152(88)90050-8")
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