Quartic: Quartic Kernel

In alan-turing-institute/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 \in (-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()

---

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.

---

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.

---

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.

---

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

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