Package 'RandVar' reference manual

Title:	Implementation of Random Variables
Description:	Implements random variables by means of S4 classes and methods.
Authors:	Matthias Kohl [cre, cph, aut], Peter Ruckdeschel [aut, cph]
Maintainer:	Matthias Kohl <[email protected]>
License:	LGPL-3
Version:	1.2.4
Built:	2024-11-03 05:42:15 UTC
Source:	https://github.com/r-forge/robast

Implementation of Random Variables

Description

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

Details

Package:	RandVar
Version:	1.2.4
Date:	2024-09-02
Depends:	R(>= 3.4), methods, distr(>= 2.8.0), distrEx(>= 2.8.0)
Imports:	startupmsg
ByteCompile:	yes
License:	LGPL-3
URL:	https://r-forge.r-project.org/projects/robast/
VCS/SVNRevision:	1261

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 [email protected],
Matthias Kohl [email protected]
Maintainer: Matthias Kohl [email protected]

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

Examples

library(RandVar)
#vignette("RandVar")
library(RandVar)
#vignette("RandVar")

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)
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 [email protected]

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))))
}
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 [email protected]

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)
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 EuclRandVariable-class

Description

Generates an object of class "EuclRandVariable".

Usage

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

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))
}
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 [email protected]

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)

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)

Generating function for EuclRandVarList-class

Description

Generates an object of class "EuclRandVarList".

Usage

EuclRandVarList(...)
EuclRandVarList(...)

Arguments

...

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

Value

Object of class "EuclRandVarList"

Author(s)

Matthias Kohl [email protected]

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(...)) 
}
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 [email protected]

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]])
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]])

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 [email protected]

Generating function for RandVariable-class

Description

Generates an object of class "RandVariable".

Usage

RandVariable(Map = list(function(x){}), Domain = NULL, Range = NULL)
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 [email protected]

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))
}
(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 [email protected]

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)
(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)
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 [email protected]

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()))
}
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 [email protected]

Examples

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

Package 'RandVar'

Help Index

Implementation of Random Variables

Description

Details

Package versions

Author(s)

References

See Also

Examples

Generating function for EuclRandMatrix-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Euclidean random matrix

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Generating function for EuclRandVariable-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Euclidean random variable

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Generating function for EuclRandVarList-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

List of Euclidean random variables

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

See Also

Examples

Optional rSpace

Description

Objects from the Class

Author(s)

See Also

Generating function for RandVariable-class

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Random variable

Description

Objects from the Class

Slots

Methods

Author(s)