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 could in principle be created by calls to new
, but more
frequently you would create them via the generating function
SphericalDistribution
.
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.
Class "MultivariateDistribution"
, directly.
Class "Distribution"
, by class "MultivariateDistribution"
.
signature(object = "SphericalDistribution")
: returns
the dimension of the distribution.
signature(object = "SphericalDistribution")
: synonym to
dimension
.
signature(object = "SphericalDistribution")
: helper
function to have the same interface as class "EllipticalDistribution"
;
always returns 0
(in the respective dimension).
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
.
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.
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.
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.
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.
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.
signature(x = "SphericalDistribution", y = "missing")
:
plot for an spherically symmetric distribution; see plot-methods
.
signature(object = "SphericalDistribution")
:
show
method for spherically symmetric distributions.
signature(object = "SphericalDistribution")
:
showobj
method for spherically symmetric distributions.
signature(object = "SphericalDistribution", fun = "missing", cond = "missing")
:
expectation of an elliptically symmetric distribution; exact.
signature(x = "SphericalDistribution")
:
expectation of an elliptically symmetric distribution; exact.
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.
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
new("SphericalDistribution") ## better use SphericalDistribution()
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