# EllipticalDistribution-class: Elliptical distribution class In distrEllipse: S4 Classes for Elliptically Contoured Distributions

## Description

Class `EllipticalDistribution` implements general elliptically symmetric distributions, i.e. starting from a spherically distribution realized as an object `S` of class `SphericalDistribution`, this is the distribution of an affine linear transformation `AS+b`.

## 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 `EllipticalDistribution`.

## Slots

`img`

Object of class `"Reals"`.

`param`

Object of class `"EllipticalParameter"`.

`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 `"EllipticalDistribution"`, 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 `"EllipticalDistribution"`, 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 `"EllipticalSymmetry"` about center `loc`; used internally to avoid unnecessary calculations.

## Extends

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

## Methods

location

`signature(object = "EllipticalDistribution")`: wrapped access method for slot `location` of slot `param`.

scale

`signature(x = "EllipticalDistribution")`: wrapped access method for slot `scale` of slot `param`.

location<-

`signature(object = "EllipticalDistribution")`: wrapped replace method for slot `location` of slot `param`.

scale<-

`signature(x = "EllipticalDistribution")`: wrapped replace method for slot `scale` of slot `param`.

E

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

E

`signature(object = "EllipticalDistribution", fun = "function", cond = "missing")`: expectation of an elliptically symmetric distribution; by simulation.

var

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

`+`

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

`-`

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

`*`

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

`%*%`

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

coerce

`signature(from = "EllipticalDistribution", to = "UnivariateDistribution")`: create a `UnivariateDistribution` object from a (one-dimensional) elliptically symmetric distribution.

coerce

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

## Author(s)

Peter Ruckdeschel [email protected]

## Examples

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

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