Elliptical distribution class

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 peter.ruckdeschel@uni-oldenburg.de

Examples

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