# 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 peter.ruckdeschel@uni-oldenburg.de

### See Also

`Parameter-class`

,
`MultivariateDistribution-class`

,
`LatticeDistribution-class`

,
`AbscontDistribution-class`

,
`simplifyD-methods`

,
`flat.mix`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
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)
``` |