Package 'distrEllipse' reference manual

Title:	S4 Classes for Elliptically Contoured Distributions
Description:	Distribution (S4-)classes for elliptically contoured distributions (based on package 'distr').
Authors:	Peter Ruckdeschel [aut, cre, cph]
Maintainer:	Peter Ruckdeschel <[email protected]>
License:	LGPL-3
Version:	2.8.3
Built:	2024-11-06 02:15:50 UTC
Source:	https://github.com/r-forge/distr

distrEllipse – S4 Classes for Elliptically Contoured Distributions

Description

distrEllipse provides infrastructure / (S4-)classes for elliptically contoured distributions (based on package distr).

Details

Package:	distrEllipse
Version:	2.8.3
Date:	2024-08-29
Depends:	R(>= 3.4), methods, graphics, mvtnorm, setRNG(>= 2006.2-1), distr(>= 2.8.0),distrEx(>= 2.8.0), distrSim(>= 2.2)
Suggests:	distrMod(>= 2.8.0), distrTEst(>= 2.2)
Imports:	startupmsg, stats
ByteCompile:	yes
License:	LGPL-3
URL:	https://distr.r-forge.r-project.org/
VCS/SVNRevision:	1455

Classes

###################################
Distribution Classes
###################################
[*]: there is a generating function with the same name
"Distribution" (from distr)
|>"MultivariateDistribution" (from distrEx)
|>|>"MultivarMixingDistribution" [*]
|>|>"SphericalDistribution" [*]
|>|>|>|>"EllipticalDistribution" [*]
|>|>|>|>"MVNormDistribution" [*]
"DistrList" (from distr)
|>"MultivarDistrList" [*/class union of "MVDistrList", "UnivarDistrList"]
|>|>"MVDistrList"
|>"UnivarDistrList" (from distr) [*]

Methods

plot-methods            Methods for Function plot
                       (for SphericalDistribution)
show-methods            Methods for Function show
                       (for Simulation/Contsimulation)

Functions

distrEllipseoptions            Functions to change the global variables of the
                        package 'distrEllipse'

Slot accessors / -replacement functions

All slots are inspected / modified by corresponding accessors / -replacement functions.

Start-up-Banner

You may suppress the start-up banner/message completely by setting options("StartupBanner"="off") somewhere before loading this package by library or require in your R-code / R-session. If option "StartupBanner" is not defined (default) or setting options("StartupBanner"=NULL) or options("StartupBanner"="complete") the complete start-up banner is displayed. For any other value of option "StartupBanner" (i.e., not in c(NULL,"off","complete")) only the version information is displayed. The same can be achieved by wrapping the library or require call into either suppressStartupMessages() or onlytypeStartupMessages(.,atypes="version").

Package versions

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the distrXXX family as a whole in order to ease updating "depends" information.

Start-up-Banner

You may suppress the start-up banner/message completely by setting options("StartupBanner"="off") somewhere before loading this package by library or require in your R-code / R-session. If option "StartupBanner" is not defined (default) or setting options("StartupBanner"=NULL) or options("StartupBanner"="complete") the complete start-up banner is displayed. For any other value of option "StartupBanner" (i.e., not in c(NULL,"off","complete")) only the version information is displayed. As for general packageStartupMessage's, you may also suppress all the start-up banner by wrapping the library or require call into suppressPackageStartupMessages() from startupmsg-version 0.5 on.

Note

Global options controlling the plots and summaries of Dataclass and Simulation/Contsimulation objects may be inspected / set by distrEllipseoptions() and getdistrEllipseOption().

Author(s)

Peter Ruckdeschel [email protected],
Maintainer: Peter Ruckdeschel [email protected]

References

P. Ruckdeschel, M. Kohl, T. Stabla, F. Camphausen (2006): S4 Classes for Distributions, R News, 6(2), 2-6. https://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf A vignette for packages distr, distrSim, distrTEst, distrEx, distrTeach, distrMod, and distrEllipse is included into the mere documentation package distrDoc and may be called by require("distrDoc");vignette("distr"). A homepage to this package is available under
https://distr.r-forge.r-project.org/.

Defunct Functions in Package distrEllipse

Description

Functions which are no longer provided in distrEllipse due to clashes with S3-method inheritance.

Methods

From version 2.7 on, former versions of S4-methods rRd, dRd, pRd, qRd, and plotRd of style <name>.rd are defunct due to clashes with S3-method inheritance. More specifically, this concerns the following methods:

r.rd: signature(object = "SphericalDistribution"): wrapped access method for slot r of slot radDistr.
d.rd: signature(object = "SphericalDistribution"): wrapped access method for slot d of slot radDistr.
p.rd: signature(object = "SphericalDistribution"): wrapped access method for slot p of slot radDistr.
q.rd: signature(object = "SphericalDistribution"): wrapped access method for slot q of slot radDistr.
plot.rd: signature(x = "SphericalDistribution"): utility; calls plot for slot radDistr.

Masking of/by other functions in package "distrEllipse"

Description

Provides information on the (intended) masking of and (non-intended) masking by other other functions in package distrEllipse

Usage

distrEllipseMASK(library = NULL)
distrEllipseMASK(library = NULL)

Arguments

library

a character vector with path names of R libraries, or NULL. The default value of NULL corresponds to all libraries currently known. If the default is used, the loaded packages are searched before the libraries

Value

no value is returned

Author(s)

Peter Ruckdeschel [email protected]

Examples

## IGNORE_RDIFF_BEGIN
distrEllipseMASK()
## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN
distrEllipseMASK()
## IGNORE_RDIFF_END

functions to change the global variables of the package ‘distrEllipse’

Description

With distrEllipseoptions and getdistrEllipseOption you may inspect and change the global variables used by package distrEllipse.

Usage

distrEllipseoptions(...)
getdistrEllipseOption(x)
distrEllipseoptions(...)
getdistrEllipseOption(x)

Arguments

`...`	any options can be defined, using name = value or by passing a list of such tagged values.
`x`	a character string holding an option name.

Details

Invoking distrEllipseoptions() with no arguments returns a list with the current values of the options. To access the value of a single option, one should use getdistrEllipseOption("WarningSim"), e.g., rather than distrEllipseoptions("WarningSim") which is a list of length one.

Value

distrEllipseoptions() returns a list of the global options of distrEllipse.
distrEllipseoptions("Nsim") returns the global option Nsim as a list of length 1.
distrEllipseoptions("Nsim" = 3000) sets the value of the global option Nsim to 3000. getdistrEllipseOption("Nsim") the current value set for option Nsim.

Currently available options

Nsim: for plotting: number of (simulated) points to be plotted.
withED: for plotting: logical; shall principal axes of the contour ellipsoid be plot in (for each panel)?
lwd.Ed: for plotting: line width of principal axes (for each panel).
col.Ed: for plotting: color of principal axes (for each panel).
withMean: for plotting: logical; shall mean be plot in (for each panel)?
cex.mean: for plotting: size of the mean symbol (for each panel).
pch.mean: for plotting: mean symbol (for each panel).
col.mean: for plotting: color of the mean symbol (for each panel).

Author(s)

Peter Ruckdeschel [email protected]

Examples

distrEllipseoptions("Nsim") # returns the value of Nsim, by default = 5
currentDistrOptions <- distrEllipseoptions()
distrEllipseoptions(Nsim = 6000)
distrEllipseoptions("Nsim")
getdistrEllipseOption("Nsim")
distrEllipseoptions(c("Nsim","withED"))
distrEllipseoptions("Nsim") # returns the value of Nsim, by default = 5
currentDistrOptions <- distrEllipseoptions()
distrEllipseoptions(Nsim = 6000)
distrEllipseoptions("Nsim")
getdistrEllipseOption("Nsim")
distrEllipseoptions(c("Nsim","withED"))

Generating function for EllipticalDistribution-class

Description

Generates an object of class "EllipticalDistribution".

Usage

EllipticalDistribution(radDistr = sqrt(Chisq(df = length(loc))),
                            loc = c(0,0), scale = diag(length(loc)), p = NULL, q = NULL)EllipticalDistribution(radDistr = sqrt(Chisq(df = length(loc))),
                            loc = c(0,0), scale = diag(length(loc)), p = NULL, q = NULL)

Arguments

`radDistr`	an object of class `UnivariateDistribution` with positive support, i.e. `p(radDistr)(0)==0`; the radial distribution.
`loc`	real number: location / center of the elliptical distribution.
`scale`	a square matrix (with `nrow(scale)==ncol(scale)==length(loc)`) of full rank: the / a scale matrix of the elliptical distribution — unique only upto `scale%%t(scale)`, i.e. if `A1` and `A2` are two square matrices of full rank such that `A1%%t(A1)==A2%*%t(A2)`, then we obtain the same elliptical distribution for `scale = A1` and for `scale = A2`.
`p`	optional: `p`-slot of the corresponding distribution;
`q`	optional: `q`-slot of the corresponding distribution;

Value

Object of class "EllipticalDistribution"

Author(s)

Peter Ruckdeschel [email protected]

Examples

E0 <- EllipticalDistribution()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)
E0 <- EllipticalDistribution()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)

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 $d \times n$ 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.

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 [email protected]

Examples

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

Paramter of an Elliptical distributions

Description

The class of the parameter of Elliptical distributions.

Objects from the Class

Objects can be created by calls of the form new("EllipticalParameter", ...).

Slots

loc: numeric; center / location of the distribution.
scale: matrix; the scale matrix; the number of rows of this matrix must be the same as the length of location.
name: default name is “parameter of a Elliptical distribution”.

Extends

Class "Parameter", directly.
Class "OptionalParameter", by class "Parameter".

Methods

location: signature(object = "EllipticalParameter"): access method for slot location.
scale: signature(x = "EllipticalParameter"): access method for slot scale.
location<-: signature(object = "EllipticalParameter"): replace method for slot location.
scale<-: signature(object = "EllipticalParameter"): replace method for slot scale.

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("EllipticalParameter")
new("EllipticalParameter")

Generating function for MultivarDistrList-class

Description

Generates an object of class "MultivarDistrList".

Usage

MultivarDistrList(..., Dlist)MultivarDistrList(..., Dlist)

Arguments

`...`	Objects of class `"MultivariateDistribution"` (or subclasses)
`Dlist`	an optional list or object of class `"MultivarDistrList"`; if not missing it is appended to argument `...`; this way `MultivarMixingDistribution` may also be called with a list (or `"MultivarDistrList"`-object) as argument as suggested in an e-mail by Krunoslav Sever (thank you!)

Value

Object of class "MVDistrList" or of class "UnivarDistrList", hence of class union "MultivarDistrList"

Author(s)

Peter Ruckdeschel [email protected]

Examples

(DL1 <- MultivarDistrList(Norm(), Exp(), Pois()))
(DL2 <- MultivarDistrList(MVNorm(),
                          EllipticalDistribution(radDistr=Exp(), loc=c(1,2),
                          scale=diag(c(3,1))),MVt()))
(DL1 <- MultivarDistrList(Norm(), Exp(), Pois()))
(DL2 <- MultivarDistrList(MVNorm(),
                          EllipticalDistribution(radDistr=Exp(), loc=c(1,2),
                          scale=diag(c(3,1))),MVt()))

List of multivariate distributions

Description

Create a list of multivariate distributions

Objects from the Class

Objects can be created by calls of the form new("MVDistrList", ...). More frequently they are created via the generating function MultivarDistrList.

Slots

.Data:: Object of class "list". A list of multivariate distributions of the same dimension.

Extends

Class "DistrList", directly.
Class "list", by class "DistrList".
Class "vector", by class "DistrList".

Methods

coerce: signature(from = "MultivariateDistribution", to = "MultivarDistrList"): create a MultivarDistrList object from a univariate distribution
dimension: dim of the range space.
dim: synonym to dimension.

Details

In fact, class "MultivarDistrList" is an inbetween class between class "DistrList" and class "UnivarDistrList", which is a case for setIs, but we would have to modify the metadata information in package distr to realize this. So we introduce a new (sister) class "MVDistrList" which implements strictly lists of multivariate distributions, and which together with "UnivarDistrList" is a subclass of the common class union class "MultivarDistrList".

Author(s)

Peter Ruckdeschel [email protected]

Examples

(DL1 <- MultivarDistrList(Norm(), Exp(), Pois()))
(DL2 <- MultivarDistrList(MVNorm(),
                          EllipticalDistribution(radDistr=Exp(), loc=c(1,2),
                          scale=diag(c(3,1))),MVt()))
(DL1 <- MultivarDistrList(Norm(), Exp(), Pois()))
(DL2 <- MultivarDistrList(MVNorm(),
                          EllipticalDistribution(radDistr=Exp(), loc=c(1,2),
                          scale=diag(c(3,1))),MVt()))

Generating function for Class "MultivarMixingDistribution"

Description

Generates an object of class "MultivarMixingDistribution".

Usage

MultivarMixingDistribution(..., Dlist, mixCoeff
                    
                    )MultivarMixingDistribution(..., Dlist, mixCoeff
                    
                    )

Arguments

`...`	Objects of class `"MultivariateDistribution"` (or subclasses)
`Dlist`	an optional list or object of class `"MultivarDistrList"`; if not missing it is appended to argument `...`; this way `MultivarMixingDistribution` may also be called with a list (or `"MultivarDistrList"`-object) as argument as suggested in an e-mail by Krunoslav Sever (thank you!)
`mixCoeff`	Objects of class `"numeric"` : a vector of probabilities for the mixing components (must be of same length as arguments in ...).

Details

If mixCoeff is missing, all elements in ... are equally weighted.

Value

Object of class "MultivarMixingDistribution", or if argument withSimplify is TRUE and the resulting object would have one mixing component with probability (almost) 1, MultivarMixingDistribution will return this component.

Author(s)

Peter Ruckdeschel [email protected]

Examples

mylist <- MultivarMixingDistribution(Binom(3,.3), Dirac(2), Norm(), 
          mixCoeff=c(1/4,1/5,11/20))
mylist <- MultivarMixingDistribution(Binom(3,.3), Dirac(2), Norm(), 
          mixCoeff=c(1/4,1/5,11/20))

Class "MultivarMixingDistribution"

Description

MultivarMixingDistribution-class is a class to formalize multivariate mixing distributions; it is a subclass to class MultivariateDistribution.

Objects from the Class

Objects can be created by calls of the form new("MultivarMixingDistribution", ...). More frequently they are created via the generating function MultivarMixingDistribution.

Slots

mixCoeff: Object of class "numeric": a vector of probabilities for the mixing components.
mixDistr: Object of class "MultivarDistrList": a list of multivariate distributions containing the mixing components; must be of same length as mixCoeff.
img: Object of class "Reals": the space of the image of this distribution which has dimension 1 and the name "Real Space"
param: Object of class "Parameter": the parameter of this distribution, having only the slot name "Parameter of a discrete distribution"
r: Object of class "function": generates random numbers
d: fixed to NULL
p: Object of class "OptionalFunction": if non-null cumulative distribution function
q: Object of class "OptionalFunction": if non-null quantile function
.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 "DistributionSymmetry"; used internally to avoid unnecessary calculations.

Extends

Class "MultivariateDistribution" class "Distribution" by class "MultivariateDistribution".

Methods

show: signature(object = "MultivarMixingDistribution") prints the object
mixCoeff<-: signature(object = "MultivarMixingDistribution") replaces the corresponding slot
mixCoeff: signature(object = "MultivarMixingDistribution") returns the corresponding slot
mixDistr<-: signature(object = "MultivarMixingDistribution") replaces the corresponding slot
mixDistr: signature(object = "MultivarMixingDistribution") returns the corresponding slot
support: signature(object = "MultivarMixingDistribution") returns the corresponding slot
gaps: signature(object = "MultivarMixingDistribution") returns the corresponding slot
.logExact: signature(object = "Distribution"): returns slot .logExact if existing; else tries to convert the object to a newer version of its class by conv2NewVersion and returns the corresponding slot of the converted object.
.lowerExact: signature(object = "Distribution"): returns slot .lowerExact if existing; else tries to convert the object to a newer version of its class by conv2NewVersion and returns the corresponding slot of the converted object.
Symmetry: returns slot Symmetry if existing; else tries to convert the object to a newer version of its class by conv2NewVersion and returns the corresponding slot of the converted object.
plot: signature(x = "MultivarMixingDistribution", y = "missing"): plot for an spherically symmetric distribution; see plot-methods.
E: corresponding expectation — see E.
dimension: dim of the range space.
dim: synonym to dimension.
show: signature(object = "MultivarMixingDistribution"): show method for spherically symmetric distributions.
showobj: signature(object = "MultivarMixingDistribution"): showobj method for spherically symmetric distributions.

Author(s)

Peter Ruckdeschel [email protected]

Examples

mylist <- MultivarMixingDistribution(Binom(3,.3), Dirac(2), Norm(), 
          mixCoeff=c(1/4,1/5,11/20))
mylist2 <- MultivarMixingDistribution(Binom(3,.3), mylist, 
          mixCoeff=c(.3,.7))
mylist2
p(mylist)(0.3)          
mixDistr(mylist2)
E(mylist)
var(mylist)

##multivariate
E1 <- diag(1,2)%*%EllipticalDistribution(radDistr=Gammad())+c(1,2)
mylistD <- MultivarMixingDistribution(MVNorm(), E1, MVt(),
          mixCoeff=c(1/4,1/5,11/20))
mylistD2 <- MultivarMixingDistribution(E1+c(-2,2), mylistD,
          mixCoeff=c(.3,.7))
mylistD2
p(mylistD)
mixDistr(mylistD2)
E(mylistD2)
var(mylistD2)
mylist <- MultivarMixingDistribution(Binom(3,.3), Dirac(2), Norm(), 
          mixCoeff=c(1/4,1/5,11/20))
mylist2 <- MultivarMixingDistribution(Binom(3,.3), mylist, 
          mixCoeff=c(.3,.7))
mylist2
p(mylist)(0.3)          
mixDistr(mylist2)
E(mylist)
var(mylist)

##multivariate
E1 <- diag(1,2)%*%EllipticalDistribution(radDistr=Gammad())+c(1,2)
mylistD <- MultivarMixingDistribution(MVNorm(), E1, MVt(),
          mixCoeff=c(1/4,1/5,11/20))
mylistD2 <- MultivarMixingDistribution(E1+c(-2,2), mylistD,
          mixCoeff=c(.3,.7))
mylistD2
p(mylistD)
mixDistr(mylistD2)
E(mylistD2)
var(mylistD2)

Generating function for MVNormDistribution-class

Description

Generates an object of class "MVNormDistribution".

Usage

MVNorm(loc=c(0,0), scale = diag(length(loc)))MVNorm(loc=c(0,0), scale = diag(length(loc)))

Arguments

`loc`	real number: location / center of the elliptical distribution.
`scale`	a square matrix (with `nrow(scale)==ncol(scale)==length(loc)`) of full rank: the / a scale matrix of the elliptical distribution — unique only upto `scale`, i.e. if `A1` and `A2` are two square matrices of full rank such that `A1%%t(A1)==A2%%t(A2)`, then we obtain the same elliptical distribution for `scale = A1` and for `scale = A2`.

Value

Object of class "MVNormDistribution"

Author(s)

Peter Ruckdeschel [email protected]

Examples

E0 <- MVNorm()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)
E0 <- MVNorm()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)

MVNorm distribution class

Description

Class MVNormDistribution implements a general multivariate distribution using code from package mvtnorm. For details to this implementation confer to the references given in this package.

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 MVNormDistribution.

Slots

img:: Object of class "Reals".
param:: Object of class "MVtParameter".
r:: function with argument n; random number generator
d:: the density of this distribution, pmvnorm
p:: the (vectorized) function pmvnorm.
q:: the (vectorized) function qmvnorm.
radDistr:: the distribution sqrt(Chisq(df=dim0))
.withArith:: FALSE
.withSim:: FALSE
.logExact:: TRUE
.lowerExact:: TRUE
Symmetry:: object of class "EllipticalSymmetry" about center loc; used internally to avoid unnecessary calculations.

Extends

Class "EllipticalDistribution", directly.
Class "SphericalDistribution", by class "EllipticalDistribution".
Class "MultivariateDistribution", by class "SphericalDistribution". Class "Distribution", by class "MultivariateDistribution".

Methods

sigma: signature(object = "MVNormDistribution"): wrapped access method for slot sigma of slot param.
mean: signature(object = "MVNormDistribution"): wrapped access method for slot location of slot param.

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("MVNormDistribution") ## better use generating function MVNormDistribution()
new("MVNormDistribution") ## better use generating function MVNormDistribution()

Paramter of a multivariate normal distribution

Description

The class of the parameter of MVNorm distributions.

Objects from the Class

Objects can be created by calls of the form new("MVNormParameter", ...).

Slots

loc:: numeric; center / location of the distribution.
scale:: matrix; the scale matrix; the number of rows of this matrix must be the same as the length of location.
name:: default name is “parameter of a Elliptical distribution”.

Extends

Class "EllipticalParameter", directly.
Class "Parameter", by class "EllipticalParameter".
Class "OptionalParameter", by class "Parameter".

Methods

mean: signature(object = "MVNormParameter"): access method for slot location.
sigma: signature(x = "MVNormParameter"): utility function; returns S%*%t(S) for S=scale(x).

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("MVNormParameter")
new("MVNormParameter")

Generating function for MvtDistribution-class

Description

Generates an object of class "MvtDistribution".

Usage

MVt(loc = c(0,0), scale = diag(length(loc)), df = 1, ncp = 0)MVt(loc = c(0,0), scale = diag(length(loc)), df = 1, ncp = 0)

Arguments

`loc`	real number: location / center of the elliptical distribution.
`scale`	a square matrix (with `nrow(scale)==ncol(scale)==length(loc)`) of full rank: the / a scale matrix of the elliptical distribution — unique only upto `scale%%t(scale)`, i.e. if `A1` and `A2` are two square matrices of full rank such that `A1%%t(A1)==A2%*%t(A2)`, then we obtain the same elliptical distribution for `scale = A1` and for `scale = A2`.
`df`	integer; degrees of freedom
`ncp`	positive real number; non-centrality parameter

Value

Object of class "MvtDistribution"

Author(s)

Peter Ruckdeschel [email protected]

Examples

E0 <- MVt()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)
E0 <- MVt()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)

MVt distribution class

Description

Class MVtDistribution implements multivariate t distributions using code from package mvtnorm. For details to this implementation confer to the references given in this package.

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 MVtDistribution.

Slots

img:

Object of class "Reals".

param:

Object of class "MVtParameter".

r:

function with argument n; random number generator

d:

the density of this distribution, dmvt

p:

the (vectorized) function pmvt.

q:

the (vectorized) function qmvt.

radDistr:

an object of class AbscontDistribution with density

${\rm dim} {({\rm dim}+{\rm df}-1)/2\choose{{\rm df}/2-1}} x^{{\rm dim}-1} {\rm df}^{-{\rm dim}/2}/ (1+x^2/{\rm df})^{({\rm dim}+{\rm df})/2}$

.withArith:

FALSE

.withSim:

FALSE

.logExact:

TRUE

.lowerExact:

TRUE

Symmetry:

object of class "EllipticalSymmetry" about center loc; used internally to avoid unnecessary calculations.

Extends

Methods

sigma: signature(object = "MVtDistribution"): wrapped access method for slot sigma of slot param.
ncp: signature(object = "MVtDistribution"): wrapped access method for slot ncp of slot param.
df: signature(x = "MVtDistribution"): wrapped access method for slot scale of slot param.

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("MVtDistribution") ## better use generating function MVtDistribution()
new("MVtDistribution") ## better use generating function MVtDistribution()

Paramter of a multivariate t distribution

Description

The class of the parameter of MVt distributions.

Objects from the Class

Objects can be created by calls of the form new("MVtParameter", ...).

Slots

loc:: numeric; center / location of the distribution.
scale:: matrix; the scale matrix; the number of rows of this matrix must be the same as the length of location.
df:: integer; the degrees of freedom.
ncp:: positive real; the non-centrality parameter.
name:: default name is “parameter of a Elliptical distribution”.

Extends

Class "Parameter", directly.
Class "OptionalParameter", by class "Parameter".

Methods

mean: signature(object = "MVnormParameter"): access method for slot location.
sigma: signature(x = "MVnormParameter"): utility function; returns S%*%t(S) for S=scale(x).
ncp: signature(object = "MVnormParameter"): access method for slot ncp.
df: signature(x = "MVnormParameter"): access method for slot df.

Author(s)

Peter Ruckdeschel [email protected]

Examples

new("MVtParameter")
new("MVtParameter")

Methods for Function plot in Package ‘distrEllipse’

Description

plot-methods

Usage

plot(x, y, ...)
## S4 method for signature 'SphericalDistribution,missing'
plot(x, Nsim = getdistrEllipseOption("Nsim"), ...,
               withED = getdistrEllipseOption("withED"),
               lwd.Ed = getdistrEllipseOption("lwd.Ed"),
               col.Ed = getdistrEllipseOption("col.Ed"),
               withMean = getdistrEllipseOption("withMean"),
               cex.mean = getdistrEllipseOption("cex.mean"),
               pch.mean = getdistrEllipseOption("pch.mean"),
               col.mean = getdistrEllipseOption("col.mean"))
## S4 method for signature 'MultivarMixingDistribution,missing'
plot(x, Nsim = getdistrEllipseOption("Nsim"), ...,
               withED = getdistrEllipseOption("withED"),
               lwd.Ed = getdistrEllipseOption("lwd.Ed"),
               col.Ed = getdistrEllipseOption("col.Ed"),
               withMean = getdistrEllipseOption("withMean"),
               cex.mean = getdistrEllipseOption("cex.mean"),
               pch.mean = getdistrEllipseOption("pch.mean"),
               col.mean = getdistrEllipseOption("col.mean"))
plot(x, y, ...)
## S4 method for signature 'SphericalDistribution,missing'
plot(x, Nsim = getdistrEllipseOption("Nsim"), ...,
               withED = getdistrEllipseOption("withED"),
               lwd.Ed = getdistrEllipseOption("lwd.Ed"),
               col.Ed = getdistrEllipseOption("col.Ed"),
               withMean = getdistrEllipseOption("withMean"),
               cex.mean = getdistrEllipseOption("cex.mean"),
               pch.mean = getdistrEllipseOption("pch.mean"),
               col.mean = getdistrEllipseOption("col.mean"))
## S4 method for signature 'MultivarMixingDistribution,missing'
plot(x, Nsim = getdistrEllipseOption("Nsim"), ...,
               withED = getdistrEllipseOption("withED"),
               lwd.Ed = getdistrEllipseOption("lwd.Ed"),
               col.Ed = getdistrEllipseOption("col.Ed"),
               withMean = getdistrEllipseOption("withMean"),
               cex.mean = getdistrEllipseOption("cex.mean"),
               pch.mean = getdistrEllipseOption("pch.mean"),
               col.mean = getdistrEllipseOption("col.mean"))

Arguments

`x`	object of class `"SphericalDistribution"` distribution to be plotted
`y`	missing
`Nsim`	number of (simulated) points to be plotted.
`withED`	logical; shall principal axes of the contour ellipsoid be plot in (for each panel)?
`lwd.Ed`	line width of principal axes (for each panel).
`col.Ed`	color of principal axes (for each panel).
`withMean`	logical; shall mean be plot in (for each panel)?
`cex.mean`	size of the mean symbol (for each panel).
`pch.mean`	mean symbol (for each panel).
`col.mean`	color of the mean symbol (for each panel).
`...`	addtional arguments for `plot` — see `plot`, `plot.default`, `plot.stepfun`

Details

Using pairs, plots all pairs of coordinates of the object, using simulated values. Any parameters of pairs may be passed on to this particular plot method.

Examples

E0 <- matrix(c(2,1,1,4),2,2)%*%EllipticalDistribution()+c(2,1)
E1 <- matrix(c(3,2,2,4),2,2)%*%EllipticalDistribution(radDistr = exp(Binom(10,.8)))
plot(E0)
plot(E1, withED=FALSE, Nsim=5000)
mylist <- MultivarMixingDistribution(E0,E1, mixCoeff=c(1/4,3/4))
plot(mylist)
E0 <- matrix(c(2,1,1,4),2,2)%*%EllipticalDistribution()+c(2,1)
E1 <- matrix(c(3,2,2,4),2,2)%*%EllipticalDistribution(radDistr = exp(Binom(10,.8)))
plot(E0)
plot(E1, withED=FALSE, Nsim=5000)
mylist <- MultivarMixingDistribution(E0,E1, mixCoeff=c(1/4,3/4))
plot(mylist)

Generating function for SphericalDistribution-class

Description

Generates an object of class "SphericalDistribution".

Usage

SphericalDistribution(radDistr = sqrt(Chisq(df=dim)), dim = 2,
                             p = NULL, q = NULL)SphericalDistribution(radDistr = sqrt(Chisq(df=dim)), dim = 2,
                             p = NULL, q = NULL)

Arguments

`radDistr`	an object of class `UnivariateDistribution` with positive support, i.e. `p(radDistr)(0)==0`; the radial distribution.
`dim`	positive integer: dimension of the distribution.
`p`	optional: `p`-slot of the corresponding distribution;
`q`	optional: `q`-slot of the corresponding distribution;

Value

Object of class "SphericalDistribution"

Author(s)

Peter Ruckdeschel [email protected]

Examples

E0 <- SphericalDistribution()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)
E0 <- SphericalDistribution()
plot(E0)
E1 <- diag(1,2)%*%E0+c(1,2)
plot(E1)
E(E1)
var(E1)

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.

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(s)

Peter Ruckdeschel [email protected]

Examples

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

Package 'distrEllipse'

Help Index

distrEllipse – S4 Classes for Elliptically Contoured Distributions

Description

Details

Classes

Methods

Functions

Slot accessors / -replacement functions

Start-up-Banner

Package versions

Start-up-Banner

Note

Author(s)

References

Defunct Functions in Package distrEllipse

Description

Methods

See Also

Masking of/by other functions in package "distrEllipse"

Description

Usage

Arguments

Value

Author(s)

Examples

functions to change the global variables of the package ‘distrEllipse’

Description

Usage

Arguments

Details

Value

Currently available options

Author(s)

See Also

Examples

Generating function for EllipticalDistribution-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Elliptical distribution class

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

Examples

Paramter of an Elliptical distributions

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Generating function for MultivarDistrList-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

List of multivariate distributions

Description

Objects from the Class

Slots

Extends

Methods

Details

Author(s)

See Also

Examples

Generating function for Class "MultivarMixingDistribution"