distr6 (version 1.5.6)

Silverman: Silverman Kernel

Description

Mathematical and statistical functions for the Silverman kernel defined by the pdf, $$f(x)=exp(-|x|/\sqrt{2})/2\ast sin(|x|/\sqrt{2}+\pi /4)$$ over the support $x\in R$.

Super classes

distr6::Distribution -> distr6::Kernel -> Silverman

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

• Silverman$new()

• Silverman$pdfSquared2Norm()

• Silverman$cdfSquared2Norm()

• Silverman$variance()

• Silverman$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$mean()

• distr6::Kernel$median()

• distr6::Kernel$mode()

• distr6::Kernel$skewness()

Method new()

Creates a new instance of this R6 class.

Usage

Silverman$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

Silverman$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

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

Usage

Silverman$variance(...)

Arguments

...

Unused.

Method clone()

The objects of this class are cloneable with this method.

Usage

Silverman$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The cdf and quantile functions are omitted as no closed form analytic expressions could be found, decorate with FunctionImputation for numeric results.

See Also

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