Silverman: Silverman Kernel

In alan-turing-institute/distr6: The Complete R6 Probability Distributions Interface

Silverman Kernel

Description

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

f(x) = exp(-|x|/\sqrt{2})/2 * sin(|x|/\sqrt{2} + \pi/4)

over the support x \in R.

Details

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

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()

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$mean()
• distr6::Kernel$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

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

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.

See Also

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

alan-turing-institute/distr6 documentation built on July 8, 2024, 4:51 p.m.