Version: 1.2.5
Date: 2025-01-12
Title: Implementation of Random Variables
Description: Implements random variables by means of S4 classes and methods.
Depends: R(≥ 3.4), methods, distr(≥ 2.8.0), distrEx(≥ 2.8.0)
Imports: startupmsg(≥ 1.0.0)
ByteCompile: yes
LazyLoad: yes
License: LGPL-3
Encoding: UTF-8
URL: https://r-forge.r-project.org/projects/robast/
LastChangedDate: {$LastChangedDate: 2025-01-12 01:01:19 +0100 (So, 12. Jan 2025) $}
LastChangedRevision: {$LastChangedRevision: 1320 $}
VCS/SVNRevision: 1319
NeedsCompilation: no
Packaged: 2025-01-12 14:34:03 UTC; kohlm
Author: Matthias Kohl ORCID iD [cre, cph, aut], Peter Ruckdeschel ORCID iD [aut, cph]
Maintainer: Matthias Kohl <Matthias.Kohl@stamats.de>
Repository: CRAN
Date/Publication: 2025-01-14 06:20:01 UTC

Implementation of Random Variables

Description

Implementation of random variables by means of S4 classes and methods.

Details

Package: RandVar
Version: 1.2.5
Date: 2025-01-12
Depends: R(>= 3.4), methods, distr(>= 2.8.0), distrEx(>= 2.8.0)
Imports: startupmsg(>= 1.0.0)
ByteCompile: yes
License: LGPL-3
URL: https://r-forge.r-project.org/projects/robast/
VCS/SVNRevision: 1319

Package versions

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

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
Maintainer: Matthias Kohl matthias.kohl@stamats.de

References

M. Kohl (2005). Numerical Contributions to the Asymptotic Theory of Robustness. Dissertation. University of Bayreuth. See also https://www.stamats.de/wp-content/uploads/2018/04/ThesisMKohl.pdf

See Also

distr-package, distrEx-package

Examples

library(RandVar)
#vignette("RandVar")

Help function for generation of image distributions

Description

Generates an imageDistribution f(distr).

Usage

.getImageDistr(f, distr)

Arguments

f

a function with values in R

distr

an object of class "Abscontdistribution"

Details

works even if f(distr) fails; if anything else fails does simulations of f(x), x according to distr; uses RtoDPQ then; does not check whether f(distr) has point masses

Value

image distribution of distr under f

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Generating function for EuclRandMatrix-class

Description

Generates an object of class "EuclRandMatrix".

Usage

EuclRandMatrix(Map = list(function(x){1}), nrow = 1, ncol = 1, 
            Domain = NULL, dimension = 1, Range)

Arguments

Map

list of functions forming the map.

nrow

number of rows.

ncol

number of columns.

Domain

object of class "OptionalrSpace": domain of Map

dimension

positive integer: dimension of the range of Map

Range

object of class "OptionalrSpace": range of Map

Value

Object of class "EuclRandMatrix"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandMatrix-class

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4}, 
           function(x){x^5}, function(x){x^6})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- EuclRandMatrix(Map = L1, nrow = 3, Domain = Reals(), dimension = 1)
R1[1:2, 2]
R1[1:2, 1:2]
Map(R1[1,2])
Map(t(R1)[2,1])

R2 <- EuclRandMatrix(Map = L2, ncol = 2, Domain = Reals(), dimension = 1)
(DL <- imageDistr(R2, Norm()))
plot(DL)

Map(gamma(R2)) # "Math" group

## "Arith" group
Map(2/R1)
Map(R2 * R2)


## The function is currently defined as
function(Map = list(function(x){1}), nrow = 1, ncol = 1,
                              Domain = NULL, dimension = 1) {
    if (missing(nrow)) 
        nrow <- ceiling(length(Map)/ncol)
    else if (missing(ncol)) 
        ncol <- ceiling(length(Map)/nrow)
    
    if(missing(Range))
        return(new("EuclRandMatrix", Map = Map, Domain = Domain, 
                   Range = EuclideanSpace(dimension = dimension),
                   Dim = as.integer(c(nrow, ncol))))
    else
        return(new("EuclRandMatrix", Map = Map, Domain = Domain, 
                   Range = Range, Dim = as.integer(c(nrow, ncol))))
}

Euclidean random matrix

Description

Class of Euclidean random matrices.

Objects from the Class

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

Slots

Dim

vector of positive integers: Dimensions of the random matrix.

Map

Object of class "list": list of functions.

Domain

Object of class "OptionalrSpace" domain of the random matrix.

Range

Object of class "OptionalrSpace" range of the random matrix.

Extends

Class "EuclRandVariable", directly.
Class "RandVariable", by class "EuclRandVariable".

Methods

coerce

signature(from = "EuclRandMatrix", to = "EuclRandVarList"): create a "EuclRandVarList" object from a Euclidean random matrix.

[

signature(x = "EuclRandMatrix"): generates a new Euclidean random variable/matrix by extracting elements of the slot Map of x.

Dim

signature(object = "EuclRandMatrix"): accessor function for slot Dim.

Dim<-

signature(object = "EuclRandMatrix", ): replacement function for slot Dim.

ncol

signature(x = "EuclRandMatrix"): number of columns of x.

nrow

signature(x = "EuclRandMatrix"): number of rows of x.

dimension

signature(object = "EuclRandMatrix"): dimension of the Euclidean random variable.

evalRandVar

signature(RandVar = "EuclRandMatrix", x = "numeric"): evaluate the slot Map of RandVar at x.

evalRandVar

signature(RandVar = "EuclRandMatrix", x = "matrix"): evaluate the slot Map of RandVar at x.

evalRandVar

signature(RandVar = "EuclRandMatrix", x = "numeric", distr = "Distribution"): evaluate the slot Map of RandVar at x assuming a probability space with distribution distr. In case x does not lie in the support of distr NA is returned.

evalRandVar

signature(RandVar = "EuclRandMatrix", x = "matrix", distr = "Distribution"): evaluate the slot Map of RandVar at rows of x assuming a probability space with distribution distr. For those rows of x which do not lie in the support of distr NA is returned.

t

signature(x = "EuclRandMatrix"): transposes x. In addition, the results of the functions in the slot Map of x are transposed.

show

signature(object = "EuclRandMatrix")

%*%

signature(x = "matrix", y = "EuclRandMatrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "numeric", y = "EuclRandMatrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandVariable", y = "EuclRandMatrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandMatrix", y = "matrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandMatrix", y = "numeric"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandMatrix", y = "EuclRandMatrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandMatrix", y = "EuclRandVariable"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

Arith

signature(e1 = "numeric", e2 = "EuclRandMatrix"): Given a numeric vector e1, a Euclidean random matrix e2 and an arithmetic operator op, the Euclidean random matrix e1 op e2 is returned.

Arith

signature(e1 = "EuclRandMatrix", e2 = "numeric"): Given a Euclidean random matrix e1, a numeric vector e2, and an arithmetic operator op, the Euclidean random matrix e1 op e2 is returned.

Arith

signature(e1 = "EuclRandMatrix", e2 = "EuclRandMatrix"): Given two Euclidean random matrices e1 and e2, and an arithmetic operator op, the Euclidean random matrix e1 op e2 is returned.

Math

signature(x = "EuclRandMatrix"): Given a "Math" group generic fct, the Euclidean random matrix fct(x) is returned.

E

signature(object = "UnivariateDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under univariate distributions.

E

signature(object = "AbscontDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under absolutely continuous univariate distributions.

E

signature(object = "DiscreteDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under discrete univariate distributions.

E

signature(object = "MultivariateDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under multivariate distributions.

E

signature(object = "DiscreteMVDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under discrete multivariate distributions.

E

signature(object = "UnivariateCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under conditional univariate distributions.

E

signature(object = "AbscontCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under absolutely continuous conditional univariate distributions.

E

signature(object = "DiscreteCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under discrete conditional univariate distributions.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandMatrix, RandVariable-class, EuclRandVariable-class, EuclRandVarList-class, Distribution-class, Arith, Math, E

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4}, 
           function(x){x^5}, function(x){x^6})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- new("EuclRandMatrix", Map = L1, Dim = as.integer(c(3,2)), 
                            Domain = Reals(), Range = Reals())
dimension(R1)
R1[1:2, 2]
R1[1:2, 1:2]
Map(R1[1,2])
Map(t(R1)[2,1])

R2 <- EuclRandMatrix(Map = L2, ncol = 2, Domain = Reals(), dimension = 1)
dimension(R2)
(DL <- imageDistr(R2, Norm()))
plot(DL)

Map(gamma(R2)) # "Math" group

## "Arith" group
Map(2/R1)
Map(R2 * R2)

Generating function for EuclRandVarList-class

Description

Generates an object of class "EuclRandVarList".

Usage

EuclRandVarList(...)

Arguments

...

Objects of class "EuclRandVariable" which shall form the list of Euclidean random variables.

Value

Object of class "EuclRandVarList"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandVarList-class

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4}, 
           function(x){x^5}, function(x){x^6})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- new("EuclRandVariable", Map = L2, Domain = Reals(), Range = Reals())
R2 <- EuclRandMatrix(Map = L1, ncol = 2, Domain = Reals(), dimension = 1)
R3 <- EuclRandMatrix(Map = L2, ncol = 2, Domain = Reals(), dimension = 1)

(RL1 <- EuclRandVarList(R1, R2, R3))
is(R1, "EuclRandVarList")
as(R1, "EuclRandVarList")
is(R2, "EuclRandVarList")
as(R2, "EuclRandVarList")

Map(exp(RL1)[[1]]) # "Math" group

## "Arith" group
Map((1 + RL1)[[1]])
Map((RL1 * 2)[[2]])
Map((RL1 / RL1)[[3]])

## The function is currently defined as
function(...){ 
    new("EuclRandVarList", list(...)) 
}

List of Euclidean random variables

Description

Create a list of Euclidean random variables

Objects from the Class

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

Slots

.Data

Object of class "list". A list of Euclidean random variables.

Extends

Class "list", from data part.
Class "vector", by class "list".

Methods

coerce

signature(from = "EuclRandVariable", to = "EuclRandVarList"): create a "EuclRandVarList" object from a Euclidean random variable.

coerce

signature(from = "EuclRandMatrix", to = "EuclRandVarList"): create a "EuclRandVarList" object from a Euclidean random matrix.

numberOfMaps

signature(object = "EuclRandVarList"): number of functions contained in the slots Map of the members of object.

dimension

signature(object = "EuclRandVarList"): dimension of the Euclidean random variable.

evalRandVar

signature(RandVar = "EuclRandVarList", x = "numeric"): evaluate the elements of RandVar at x.

evalRandVar

signature(RandVar = "EuclRandVarList", x = "matrix"): evaluate the elements of RandVar at rows of x.

evalRandVar

signature(RandVar = "EuclRandVarList", x = "numeric", distr = "Distribution"): evaluate the elements of RandVar at x assuming a probability space with distribution distr. In case x does not lie in the support of distr NA is returned.

evalRandVar

signature(RandVar = "EuclRandVarList", x = "matrix", distr = "Distribution"): evaluate the elements of RandVar at rows of x assuming a probability space with distribution distr. For those rows of x which do not lie in the support of distr NA is returned.

imageDistr

signature(RandVar = "EuclRandVarList", distr = "Distribution"): image distribution of distr under RandVar. Returns an object of class "DistrList".

show

signature(object = "EuclRandVarList")

t

signature(x = "EuclRandVarList"): returns an object of class "EuclRandVarList" where the rhe results of the functions in the slots Map of the members of x are transposed.

%m%

signature(x = "EuclRandVarList", y = "EuclRandVarList"): matrix multiplication for objects of class "EuclRandVarList". Generates an object of class "EuclRandVarList".

%*%

signature(x = "matrix", y = "EuclRandVarList"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandVarList", y = "matrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

Arith

signature(e1 = "numeric", e2 = "EuclRandVarList"): Given a numeric vector e1, a list of Euclidean random variables e2 and an arithmetic operator op, the list of Euclidean random variables e1 op e2 is returned.

Arith

signature(e1 = "EuclRandVarList", e2 = "numeric"): Given a numeric vector e2, a list of Euclidean random variables e1 and an arithmetic operator op, the list of Euclidean random variables e1 op e2 is returned.

Arith

signature(e1 = "EuclRandVarList", e2 = "EuclRandVarList"): Given two lists of Euclidean random variables e1, e2 and an arithmetic operator op, the list of Euclidean random variables e1 op e2 is returned.

Math

signature(x = "EuclRandVarList"): Given a "Math" group generic fct, the list of Euclidean random variables fct(x) is returned.

E

signature(object = "UnivariateDistribution", fun = "EuclRandVarList", cond = "missing"): expectation of fun under univariate distributions.

E

signature(object = "AbscontDistribution", fun = "EuclRandVarList", cond = "missing"): expectation of fun under absolutely continuous univariate distributions.

E

signature(object = "DiscreteDistribution", fun = "EuclRandVarList", cond = "missing"): expectation of fun under discrete univariate distributions.

E

signature(object = "MultivariateDistribution", fun = "EuclRandVarList", cond = "missing"): expectation of fun under multivariate distributions.

E

signature(object = "DiscreteMVDistribution", fun = "EuclRandVarList", cond = "missing"): expectation of fun under discrete multivariate distributions.

E

signature(object = "UnivariateCondDistribution", fun = "EuclRandVarList", cond = "numeric"): expectation of fun under conditional univariate distributions.

E

signature(object = "AbscontCondDistribution", fun = "EuclRandVarList", cond = "numeric"): expectation of fun under absolutely continuous conditional univariate distributions.

E

signature(object = "DiscreteCondDistribution", fun = "EuclRandVarList", cond = "numeric"): expectation of fun under discrete conditional univariate distributions.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandMatrix, RandVariable-class, EuclRandVariable-class, EuclRandMatrix-class, Distribution-class, Arith, Math, E

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4}, 
           function(x){x^5}, function(x){x^6})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- new("EuclRandVariable", Map = L2, Domain = Reals(), Range = Reals())
R2 <- EuclRandMatrix(Map = L1, ncol = 2, Domain = Reals(), dimension = 1)
R3 <- EuclRandMatrix(Map = L2, ncol = 2, Domain = Reals(), dimension = 1)

(RL1 <- new("EuclRandVarList", list(R1, R2, R3)))
dimension(RL1)
as(R1, "EuclRandVarList")
as(R2, "EuclRandVarList")

Map(exp(RL1)[[1]]) # "Math" group

## "Arith" group
Map((1 + RL1)[[1]])
Map((RL1 * 2)[[2]])
Map((RL1 / RL1)[[3]])

Generating function for EuclRandVariable-class

Description

Generates an object of class "EuclRandVariable".

Usage

EuclRandVariable(Map = list(function(x){1}), Domain = NULL, 
                 dimension = 1, Range)

Arguments

Map

list of functions forming the map.

Domain

object of class "OptionalrSpace": domain of Map

dimension

positive integer: dimension of the range of Map

Range

object of class "OptionalrSpace": range of Map

Value

Object of class "EuclRandVariable"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandVariable-class

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- EuclRandVariable(Map = L1, Domain = Reals(), dimension = 1)
Map(R1)
Range(R1)
Range(R1) <- Reals()
R1[2]
Map(R1[3])
Map(R1[c(1,2,4)])
Map(R1[2:4])
set.seed(123)
evalRandVar(R1, rnorm(1))
x <- as.matrix(rnorm(10))
res.R1 <- evalRandVar(R1, x)
res.R1[2,,] # results for Map(R1)[[2]](x)
res.R1[2,1,] # results for Map(R1)[[2]](x[1,])

R2 <- EuclRandVariable(L2, Domain = Reals(), dimension = 1)
DL1 <- imageDistr(R2, Norm())
plot(DL1)

Domain(R2) <- EuclideanSpace(dimension = 2)
Range(R2) <- EuclideanSpace(dimension = 2)
(X <- matrix(c(x, rnorm(10)), ncol = 2))
res.R2 <- evalRandVar(R2, X)
res.R2[3,,1] # results for Map(R2)[[3]](X[,1])

Map(log(abs(R2))) # "Math" group generic

# "Arith" group generic
Map(3 + R1)
Map(c(1,3,5) * R1)
try(1:5 * R1) # error
Map(1:2 * R2)
Map(R2 - 5)
Map(R1 ^ R1)


## The function is currently defined as
function(Map = list(function(x){1}), Domain = NULL, dimension = 1, Range) {
    if(missing(Range))
        return(new("EuclRandVariable", Map = Map, Domain = Domain, 
                   Range = EuclideanSpace(dimension = dimension)))
    else
        return(new("EuclRandVariable", Map = Map, Domain = Domain, 
                   Range = Range))
}

Euclidean random variable

Description

Class of Euclidean random variables.

Objects from the Class

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

Slots

Map

Object of class "list": list of functions.

Domain

Object of class "OptionalrSpace": domain of the random variable.

Range

Object of class "EuclideanSpace": range of the random variable.

Extends

Class "RandVariable", directly.

Methods

coerce

signature(from = "EuclRandVariable", to = "EuclRandMatrix"): create a "EuclRandMatrix" object from a Euclidean random variable.

coerce

signature(from = "EuclRandVariable", to = "EuclRandVarList"): create a "EuclRandVarList" object from a Euclidean random variable.

Range<-

signature(object = "EuclRandVariable"): replacement function for the slot Range.

[

signature(x = "EuclRandVariable"): generates a new Euclidean random variable by extracting elements of the slot Map of x.

evalRandVar

signature(RandVar = "EuclRandVariable", x = "numeric", distr = "missing"): evaluate the slot Map of RandVar at x.

evalRandVar

signature(RandVar = "EuclRandVariable", x = "matrix", distr = "missing"): evaluate the slot Map of RandVar at rows of x.

evalRandVar

signature(RandVar = "EuclRandVariable", x = "numeric", distr = "Distribution"): evaluate the slot Map of RandVar at x assuming a probability space with distribution distr. In case x does not lie in the support of distr NA is returned.

evalRandVar

signature(RandVar = "EuclRandVariable", x = "matrix", distr = "Distribution"): evaluate the slot Map of RandVar at rows of x assuming a probability space with distribution distr. For those rows of x which do not lie in the support of distr NA is returned.

imageDistr

signature(RandVar = "EuclRandVariable", distr = "Distribution"): image distribution of distr under RandVar. Returns an object of class "DistrList".

dimension

signature(object = "EuclRandVariable"): dimension of the Euclidean random variable.

t

signature(x = "EuclRandVariable"): returns an object of class "EuclRandMatrix" where the rhe results of the functions in the slot Map of x are transposed.

%*%

signature(x = "matrix", y = "EuclRandVariable"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandVariable", y = "matrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "numeric", y = "EuclRandVariable"): generates an object of class "EuclRandMatrix" (1 x 1 matrix) by multiplying (scalar/innner product) x and y.

%*%

signature(x = "EuclRandVariable", y = "numeric"): generates an object of class "EuclRandMatrix" (1 x 1 matrix) by multiplying (scalar/innner product) x and y.

%*%

signature(x = "EuclRandVariable", y = "EuclRandVariable"): generates an object of class "EuclRandMatrix" (1 x 1 matrix) by multiplying (scalar/innner product) x and y.

%*%

signature(x = "EuclRandVariable", y = "EuclRandMatrix"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

%*%

signature(x = "EuclRandMatrix", y = "EuclRandVariable"): matrix multiplication of x and y. Generates an object of class "EuclRandMatrix".

Arith

signature(e1 = "numeric", e2 = "EuclRandVariable"): Given a numeric vector e1, a Euclidean random variable e2 and an arithmetic operator op, the Euclidean random variable e1 op e2 is returned.

Arith

signature(e1 = "EuclRandVariable", e2 = "numeric"): Given a numeric vector e2, a Euclidean random variable e1 and an arithmetic operator op, the Euclidean random variable e1 op e2 is returned.

Arith

signature(e1 = "EuclRandVariable", e2 = "EuclRandVariable"): Given two Euclidean random variables e1, e2 and an arithmetic operator op, the Euclidean random variable e1 op e2 is returned.

Math

signature(x = "EuclRandVariable"): Given a "Math" group generic fct, the Euclidean random variable fct(x) is returned.

E

signature(object = "UnivariateDistribution", fun = "EuclRandVariable", cond = "missing"): expectation of fun under univariate distributions.

E

signature(object = "AbscontDistribution", fun = "EuclRandVariable", cond = "missing"): expectation of fun under absolutely continuous univariate distributions.

E

signature(object = "DiscreteDistribution", fun = "EuclRandVariable", cond = "missing"): expectation of fun under discrete univariate distributions.

E

signature(object = "MultivariateDistribution", fun = "EuclRandVariable", cond = "missing"): expectation of fun under multivariate distributions.

E

signature(object = "DiscreteMVDistribution", fun = "EuclRandVariable", cond = "missing"): expectation of fun under discrete multivariate distributions.

E

signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"): conditional expectation of fun under conditional univariate distributions.

E

signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"): conditional expectation of fun under absolutely continuous conditional univariate distributions.

E

signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"): conditional expectation of fun under discrete conditional univariate distributions.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandVariable, RandVariable-class, EuclRandMatrix-class, EuclRandVarList-class, Distribution-class, Arith, Math, E

Examples

L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4})
L2 <- list(function(x){exp(x)}, function(x){abs(x)}, 
           function(x){sin(x)}, function(x){floor(x)})

R1 <- new("EuclRandVariable", Map = L1, Domain = Reals(), Range = Reals())
dimension(R1)
Map(R1)
Range(R1)
R1[2]
Map(R1[3])
Map(R1[c(1,2,4)])
Map(R1[2:4])
set.seed(123)
evalRandVar(R1, rnorm(1))
x <- as.matrix(rnorm(10))
res.R1 <- evalRandVar(R1, x)
res.R1[2,,] # results for Map(R1)[[2]](x)
res.R1[2,1,] # results for Map(R1)[[2]](x[1,])

R2 <- EuclRandVariable(L2, Domain = Reals(), dimension = 1)
dimension(R2)
DL1 <- imageDistr(R2, Norm())
plot(DL1)

Domain(R2) <- EuclideanSpace(dimension = 2)
Range(R2) <- EuclideanSpace(dimension = 2)
dimension(R2)
(X <- matrix(c(x, rnorm(10)), ncol = 2))
res.R2 <- evalRandVar(R2, X)
res.R2[3,,1] # results for Map(R2)[[3]](X[,1])

Map(log(abs(R2))) # "Math" group generic

# "Arith" group generic
Map(3 + R1)
Map(c(1,3,5) * R1)
try(1:5 * R1) # error
Map(1:2 * R2)
Map(R2 - 5)
Map(R1 ^ R1)

Optional rSpace

Description

Optional object of class "rSpace".

Objects from the Class

A virtual Class: No objects may be created from it.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

rSpace-class

Generating function for RandVariable-class

Description

Generates an object of class "RandVariable".

Usage

RandVariable(Map = list(function(x){}), Domain = NULL, Range = NULL)

Arguments

Map

list of functions forming the map.

Domain

domain of Map: object of class "OptionalrSpace" (default = NULL).

Range

range of Map: object of class "OptionalrSpace" (default = NULL).

Value

Object of class "RandVariable"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

RandVariable-class

Examples

(R1 <- RandVariable())
Map(R1)
Domain(R1)
Range(R1)
Map(R1) <- list(function(x){ceiling(x)}, function(x){floor(x)})
Domain(R1) <- Reals()
Range(R1) <- Naturals()
R1
Map(R1)
length(R1)

R2 <- R1
Domain(R2) <- Naturals()
compatibleDomains(R1, R2)
Domain(R2) <- NULL
compatibleDomains(R1, R2)
Domain(R2) <- EuclideanSpace(dimension = 1)
compatibleDomains(R1, R2)
Domain(R2) <- EuclideanSpace(dimension = 2)
compatibleDomains(R1, R2)

## The function is currently defined as
function(Map = list(function(x){ }), Domain = NULL, Range = NULL) {
    return(new("RandVariable", Map = Map, Domain = Domain, Range = Range))
}

Random variable

Description

Class of random variables; i.e., measurable maps from Domain to Range. The elements contained in the list Map are functions in one(!) argument named “x”.

Objects from the Class

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

Slots

Map

Object of class "list": list of functions.

Domain

Object of class "OptionalrSpace": domain of the random variable.

Range

Object of class "OptionalrSpace": range of the random variable.

Methods

Map

signature(object = "RandVariable"): accessor function for the slot Map.

Domain

signature(object = "RandVariable"): accessor function for the slot Domain.

Range

signature(object = "RandVariable"): accessor function for the slot Range.

Map<-

signature(object = "RandVariable"): replacement function for the slot Map.

Domain<-

signature(object = "RandVariable"): replacement function for the slot Domain.

Range<-

signature(object = "RandVariable"): replacement function for the slot Range.

compatibleDomains

signature(e1 = "RandVariable", e2 = "RandVariable"): test if the domains of two random variables are compatible.

length

signature(object = "RandVariable"): length of the list of functions in slot Map.

show

signature(object = "RandVariable")

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

RandVariable, EuclRandVariable-class, EuclRandMatrix-class, EuclRandVarList-class

Examples

(R1 <- new("RandVariable"))
Map(R1)
Domain(R1)
Range(R1)
Map(R1) <- list(function(x){ceiling(x)}, function(x){floor(x)})
Domain(R1) <- Reals()
Range(R1) <- Naturals()
R1
Map(R1)
length(R1)

R2 <- R1
Domain(R2) <- Naturals()
compatibleDomains(R1, R2)
Domain(R2) <- NULL
compatibleDomains(R1, R2)
Domain(R2) <- EuclideanSpace(dimension = 1)
compatibleDomains(R1, R2)
Domain(R2) <- EuclideanSpace(dimension = 2)
compatibleDomains(R1, R2)

Generating function for RealRandVariable-class

Description

Generates an object of class "RealRandVariable".

Usage

RealRandVariable(Map = list(function(x) {1}), Domain = NULL, Range)

Arguments

Map

list of functions forming the map.

Domain

domain of Map: object of class "OptionalrSpace".

Range

range of Map: object of class "Reals".

Value

Object of class "RealRandVariable"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

RealRandVariable-class

Examples

RealRandVariable(Map = list(function(x){x}), Domain = Reals())

## The function is currently defined as
function(Map = list(function(x){1}), Domain = NULL, Range) {
    if(missing(Range)) Range <- Reals()
    if(!is(Range, "Reals"))
        stop("'Range' has to be of class 'Reals'")

    return(new("RealRandVariable", Map = Map, 
               Domain = Domain, Range = Reals()))
}

Real random variable

Description

Class of real random variables.

Objects from the Class

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

Slots

Map

Object of class "list": list of functions.

Domain

Object of class "OptionalrSpace": domain of the random variable.

Range

Object of class "Reals": range of the random variable.

Extends

Class "EuclRandVariable", directly.
Class "RandVariable", by class "EuclRandVariable".

Methods

Range<-

signature(object = "EuclRandVariable"): replacement function for the slot Range.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

See Also

EuclRandVariable-class

Examples

new("RealRandVariable", Map=list(function(x){x}), Range = Reals())