SphericalDistribution-class: Spherical distribution class

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.

Arguments

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 \(d \times n\) p(object)(q) returns, for each of the n columns \(P(X_i\leq q_i,\;i=1,\ldots,d)\).
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 \(P(X_i\leq q_j,\;i=1,\ldots,d)\ge p_j\).
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 2.7 on, replaces defunct r.Rd to avoid clashes with S3-method inheritance.
dRd: signature(object = "SphericalDistribution"): wrapped access method for slot d of slot radDistr. From version 2.7 on, replaces defunct d.Rd to avoid clashes with S3-method inheritance.
pRd: signature(object = "SphericalDistribution"): wrapped access method for slot p of slot radDistr. From version 2.7 on, replaces defunct p.Rd to avoid clashes with S3-method inheritance.
qRd: signature(object = "SphericalDistribution"): wrapped access method for slot q of slot radDistr. From version 2.7 on, replaces defunct 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

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Examples

Run this code

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

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