Normal Kernel

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

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

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()

Inherited methods

• distr6::Distribution$cdf()
• distr6::Distribution$confidence()
• 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()

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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.

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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.

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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

NormalKernel$variance(...)

Arguments

...

Unused.

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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.