distr6 (version 1.5.2)

NormalKernel: Normal Kernel

Description

Mathematical and statistical functions for the NormalKernel kernel defined by the pdf, $$f(x)=exp(-x^2/2)/\sqrt{2\pi }$$ over the support $x\in \text{R}$.

Super classes

distr6::Distribution -> distr6::Kernel -> NormalKernel

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

packages

Packages required to be installed in order to construct the distribution.

Methods

Public methods

• NormalKernel$new()

• NormalKernel$pdfSquared2Norm()

• NormalKernel$variance()

• NormalKernel$clone()

• distr6::Distribution$cdf()

• distr6::Distribution$correlation()

• distr6::Distribution$getParameterValue()

• distr6::Distribution$iqr()

• distr6::Distribution$liesInSupport()

• distr6::Distribution$liesInType()

• distr6::Distribution$parameters()

• distr6::Distribution$pdf()

• distr6::Distribution$prec()

• distr6::Distribution$print()

• distr6::Distribution$quantile()

• distr6::Distribution$rand()

• distr6::Distribution$setParameterValue()

• distr6::Distribution$stdev()

• distr6::Distribution$strprint()

• distr6::Distribution$summary()

• distr6::Distribution$workingSupport()

• distr6::Kernel$cdfSquared2Norm()

• distr6::Kernel$mean()

• distr6::Kernel$median()

• distr6::Kernel$mode()

• distr6::Kernel$skewness()

Method new()

Creates a new instance of this R6 class.

Usage

NormalKernel$new(decorators = NULL)

Arguments

decorators

(character()) Decorators to add to the distribution during construction.

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

NormalKernel$pdfSquared2Norm(x = 0, upper = Inf)

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 $$va{r}_X=E[X^2]-E[X{]}^2$$ where $E_X$ is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

NormalKernel$variance(...)

Arguments

...

Unused.

Method clone()

The objects of this class are cloneable with this method.

Usage

NormalKernel$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

We use the erf and erfinv error and inverse error functions from pracma.

See Also

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