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 could in principle be created by calls to new
, but more
frequently you would create them via the generating function
EllipticalDistribution
.
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 \(d \times n\) 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
"EllipticalDistribution"
,
for p
a vector of length \(n\), returns, for each of the
n
components the infinimal number \(q_j\) such that
\(P(X_i\leq q_j,\;i=1,\ldots,d)\ge p_j\).
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 "EllipticalSymmetry"
about
center loc
; used internally to avoid unnecessary calculations.
Class "SphericalDistribution"
, directly.
Class "MultivariateDistribution"
, by class "SphericalDistribution"
.
Class "Distribution"
, by class "MultivariateDistribution"
.
signature(object = "EllipticalDistribution")
: wrapped access method for
slot location
of slot param
.
signature(x = "EllipticalDistribution")
: wrapped access method for
slot scale
of slot param
.
signature(object = "EllipticalDistribution")
: wrapped replace method for
slot location
of slot param
.
signature(x = "EllipticalDistribution")
: wrapped replace method for
slot scale
of slot param
.
signature(object = "EllipticalDistribution", fun = "missing", cond = "missing")
:
expectation of an elliptically symmetric distribution; exact.
signature(object = "EllipticalDistribution", fun = "function", cond = "missing")
:
expectation of an elliptically symmetric distribution; by simulation.
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.
signature(from = "EllipticalDistribution", to = "UnivariateDistribution")
:
create a UnivariateDistribution
object from a (one-dimensional)
elliptically symmetric distribution.
signature(from = "UnivariateDistribution", to = "EllipticalDistribution")
:
create a EllipticalDistribution
object from a (symmetric)
univariate distribution.
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
new("EllipticalDistribution") ## better use EllipticalDistribution()
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