Sigmoid: Sigmoid Kernel

In RaphaelS1/distr6: The Complete R6 Probability Distributions Interface

Sigmoid Kernel

Description

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

f(x) = 2/\pi(exp(x) + exp(-x))^{-1}

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 -> Sigmoid

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

• Sigmoid$new()

• Sigmoid$pdfSquared2Norm()

• Sigmoid$variance()

• Sigmoid$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

Sigmoid$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

Sigmoid$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

Sigmoid$variance(...)

Arguments

...

Unused.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Sigmoid$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

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

RaphaelS1/distr6 documentation built on Feb. 24, 2024, 9:14 p.m.