Spherical distribution class

Share:

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).

radDistr

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 peter.ruckdeschel@uni-oldenburg.de

Examples

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