# SphericalDistribution-class: Spherical distribution class In distrEllipse: S4 Classes for Elliptically Contoured Distributions

## Description

Class `SphericalDistribution` implements general spherically symmetric distributions, i.e. starting from a random variable `L` distributed according to a univariate distribution `radDistr` with positive support serving as radial distribution, and an independent random variable `U` distributed uniformly on the `dim` dimensional sphere, this is the distribution of `LU`.

## Objects from the Class

Objects could in principle be created by calls to `new`, but more frequently you would create them via the generating function `SphericalDistribution`.

## Slots

`img`

Object of class `"Reals"`.

`param`

Object of class `"SphericalParameter"`.

`r`

function with argument `n`; random number generator

`d`

optional function; in case it exists: the density of the distribution

`p`

optional function; in case it is non-null: the cdf of the distribution evaluated on rectangles, i.e. if a random variable `X` is distributed according to an `object` of class `"SphericalDistribution"`, for `q` a matrix of dimension d x n `p(object)(q)` returns, for each of the `n` columns P(X[i]<= q[i],\;i=1,…,d).

`q`

optional function; in case it is non-null: the quantile of the distribution evaluated on rectangles, i.e. if a random variable `X` is distributed according to an `object` of class `"SphericalDistribution"`, for `p` a vector of length n, returns, for each of the `n` components the infinimal number q[j] such that P(X[i]<= q[j],\;i=1,…,d)>= p[j].

`radDistr`

an object of class `UnivariateDistribution` with positive support, i.e. `p(radDistr)(0)==0`; the radial distribution.

`.withArith`

logical: used internally to issue warnings as to interpretation of arithmetics

`.withSim`

logical: used internally to issue warnings as to accuracy

`.logExact`

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

`.lowerExact`

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

`Symmetry`

object of class `"SphericalSymmetry"` about center `loc`; used internally to avoid unnecessary calculations.

## Extends

Class `"MultivariateDistribution"`, directly.
Class `"Distribution"`, by class `"MultivariateDistribution"`.

## Methods

dimension

`signature(object = "SphericalDistribution")`: returns the dimension of the distribution.

dim

`signature(object = "SphericalDistribution")`: synonym to `dimension`.

location

`signature(object = "SphericalDistribution")`: helper function to have the same interface as class `"EllipticalDistribution"`; always returns `0` (in the respective dimension).

scale

`signature(object = "SphericalDistribution")`: helper function to have the same interface as class `"EllipticalDistribution"`; always returns the unit matrix (in the respective dimension).

`signature(object = "SphericalDistribution")`: access method for slot `radDistr`.

rRd

`signature(object = "SphericalDistribution")`: wrapped access method for slot `r` of slot `radDistr`. From version 2.6 on, replaces deprecated `r.Rd` to avoid clashes with S3-method inheritance.

dRd

`signature(object = "SphericalDistribution")`: wrapped access method for slot `d` of slot `radDistr`. From version 2.6 on, replaces deprecated `d.Rd` to avoid clashes with S3-method inheritance.

pRd

`signature(object = "SphericalDistribution")`: wrapped access method for slot `p` of slot `radDistr`. From version 2.6 on, replaces deprecated `p.Rd` to avoid clashes with S3-method inheritance.

qRd

`signature(object = "SphericalDistribution")`: wrapped access method for slot `q` of slot `radDistr`. From version 2.6 on, replaces deprecated `q.Rd` to avoid clashes with S3-method inheritance.

plotRd

`signature(x = "SphericalDistribution")`: utility; calls `plot` for slot `radDistr`. From version 2.6 on, replaces deprecated `plot.Rd` to avoid clashes with S3-method inheritance.

plot

`signature(x = "SphericalDistribution", y = "missing")`: plot for an spherically symmetric distribution; see `plot-methods`.

show

`signature(object = "SphericalDistribution")`: `show` method for spherically symmetric distributions.

showobj

`signature(object = "SphericalDistribution")`: `showobj` method for spherically symmetric distributions.

E

`signature(object = "SphericalDistribution", fun = "missing", cond = "missing")`: expectation of an elliptically symmetric distribution; exact.

var

`signature(x = "SphericalDistribution")`: expectation of an elliptically symmetric distribution; exact.

coerce

`signature(from = "SphericalDistribution", to = "EllipticalDistribution")`: create a `EllipticalDistribution` object from a spherically symmetric distribution.

`+`

`signature(e1 = "SphericalDistribution", e2 = "numeric")`: affine linear transformation; exact.

`-`

`signature(e1 = "SphericalDistribution", e2 = "numeric")`: affine linear transformation; exact.

`-`

`signature(e1 = "SphericalDistribution", e2 = "missing")`: affine linear transformation; exact.

`*`

`signature(e1 = "SphericalDistribution", e2 = "numeric")`: affine linear transformation; exact.

`+`

`signature(e1 = "numeric", e2 = "SphericalDistribution")`: affine linear transformation; exact.

`-`

`signature(e1 = "numeric", e2 = "SphericalDistribution")`: affine linear transformation; exact.

`*`

`signature(e1 = "numeric", e2 = "SphericalDistribution")`: affine linear transformation; exact.

`%*%`

`signature(e1 = "numeric", e2 = "SphericalDistribution")`: affine linear transformation; exact.

## Author(s)

Peter Ruckdeschel [email protected]

## Examples

 `1` ```new("SphericalDistribution") ## better use SphericalDistribution() ```

distrEllipse documentation built on May 29, 2017, 1:13 p.m.