Quartic: Quartic Kernel

In distr6: The Complete R6 Probability Distributions Interface

Quartic Kernel

Description

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

f(x) = 15/16(1 - x^2)^2

over the support x ε (-1,1).

Details

Quantile is omitted as no closed form analytic expression could be found, decorate with FunctionImputation for numeric results.

Super classes

distr6::Distribution -> distr6::Kernel -> Quartic

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

• Quartic$pdfSquared2Norm()

• Quartic$cdfSquared2Norm()

• Quartic$variance()

• Quartic$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$initialize()

• distr6::Kernel$mean()

• distr6::Kernel$median()

• distr6::Kernel$mode()

• distr6::Kernel$skewness()

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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

Quartic$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 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

Quartic$cdfSquared2Norm(x = 0, upper = 0)

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

Quartic$variance(...)

Arguments

...

Unused.

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Method clone()

The objects of this class are cloneable with this method.

Usage

Quartic$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

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

distr6 documentation built on March 28, 2022, 1:05 a.m.