Mathematical and statistical functions for the Triweight kernel defined by the pdf, $$f(x) = 35/32(1 - x^2)^3$$ over the support \(x \in (-1,1)\).

Details

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

Super classes

distr6::Distribution -> distr6::Kernel -> Triweight

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Inherited methods


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

Triweight$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

Triweight$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

Triweight$variance(...)

Arguments

...

Unused.


Method clone()

The objects of this class are cloneable with this method.

Usage

Triweight$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.