Package elki.math.statistics.kernelfunctions

Class EpanechnikovKernelDensityFunction

java.lang.Object

elki.math.statistics.kernelfunctions.EpanechnikovKernelDensityFunction

All Implemented Interfaces:

KernelDensityFunction

@Alias("epanechnikov")
public final class EpanechnikovKernelDensityFunction
extends java.lang.Object
implements KernelDensityFunction

Epanechnikov kernel density estimator.

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	EpanechnikovKernelDensityFunction.Par	Parameterization stub.

Field Summary

Fields

Modifier and Type	Field	Description
static double	CANONICAL_BANDWIDTH	Canonical bandwidth: 15^(1/5)
static EpanechnikovKernelDensityFunction	KERNEL	Static instance.
static double	R	R constant.
static double	STDDEV	Standard deviation.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	EpanechnikovKernelDensityFunction()	Private, empty constructor.

Method Summary

Modifier and Type	Method	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
double	standardDeviation()	Get the standard deviation of the kernel function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

KERNEL

public static final EpanechnikovKernelDensityFunction KERNEL

Static instance.

CANONICAL_BANDWIDTH

@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")
public static final double CANONICAL_BANDWIDTH

Canonical bandwidth: 15^(1/5)

STDDEV

public static final double STDDEV

Standard deviation.

R

public static final double R

R constant.

See Also:

Constant Field Values

Constructor Detail

EpanechnikovKernelDensityFunction

private EpanechnikovKernelDensityFunction()

Private, empty constructor. Use the static instance!

Method Detail

density

public double density(double delta)

Description copied from interface: KernelDensityFunction

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))

Specified by:

density in interface KernelDensityFunction

Parameters:

delta - Relative distance

Returns:

density contribution

canonicalBandwidth

public double canonicalBandwidth()

Description copied from interface: KernelDensityFunction

Get the canonical bandwidth for this kernel.

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

Specified by:

canonicalBandwidth in interface KernelDensityFunction

Returns:

Canonical bandwidth

standardDeviation

public double standardDeviation()

Description copied from interface: KernelDensityFunction

Get the standard deviation of the kernel function.

Specified by:

standardDeviation in interface KernelDensityFunction

Returns:

Standard deviation

getR

public double getR()

Description copied from interface: KernelDensityFunction

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

TODO: any better name for this?

Specified by:

getR in interface KernelDensityFunction

Returns:

R value