Epanechnikov: Epanechnikov Kernel

Description Details Super classes Public fields Methods See Also

Description

Mathematical and statistical functions for the Epanechnikov kernel defined by the pdf,

f(x) = 3/4(1-x^2)

over the support x ε (-1,1).

Details

The quantile function is omitted as no closed form analytic expressions could be found, decorate with FunctionImputation for numeric results.

Super classes

distr6::Distribution -> distr6::Kernel -> Epanechnikov

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

Inherited methods

Method pdfSquared2Norm()

The squared 2-norm of the pdf is defined by

\int_a^b (f_X(u))^2 du

where X is the Distribution, f_X is its pdf and a, b are the distribution support limits.

Usage
Epanechnikov$pdfSquared2Norm(x = 0, upper = Inf)
Arguments
x

(numeric(1))
Amount to shift the result.

upper

(numeric(1))
Upper limit of the integral.


Method cdfSquared2Norm()

The squared 2-norm of the cdf is defined by

\int_a^b (F_X(u))^2 du

where X is the Distribution, F_X is its pdf and a, b are the distribution support limits.

Usage
Epanechnikov$cdfSquared2Norm(x = 0, upper = 0)
Arguments
x

(numeric(1))
Amount to shift the result.

upper

(numeric(1))
Upper limit of the integral.


Method variance()

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage
Epanechnikov$variance(...)
Arguments
...

Unused.


Method clone()

The objects of this class are cloneable with this method.

Usage
Epanechnikov$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

See Also

Other kernels: Cosine, LogisticKernel, NormalKernel, Quartic, Sigmoid, Silverman, TriangularKernel, Tricube, Triweight, UniformKernel


distr6 documentation built on Sept. 6, 2021, 9:10 a.m.