EuclRandVariable-class {RandVar}

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 [e-mail]

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)