Euclidean random variable
Class of Euclidean random variables.
Objects can be created by calls of the form new("EuclRandVariable", ...).
More frequently they are created via the generating function
EuclRandVariable.
MapObject of class "list": list of functions.
DomainObject of class "OptionalrSpace":
domain of the random variable.
RangeObject of class "EuclideanSpace":
range of the random variable.
Class "RandVariable", directly.
signature(from = "EuclRandVariable", to = "EuclRandMatrix"):
create a "EuclRandMatrix" object from a Euclidean random variable.
signature(from = "EuclRandVariable", to = "EuclRandVarList"):
create a "EuclRandVarList" object from a Euclidean random variable.
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.
signature(RandVar = "EuclRandVariable", x = "numeric", distr = "missing"):
evaluate the slot Map of RandVar at x.
signature(RandVar = "EuclRandVariable", x = "matrix", distr = "missing"):
evaluate the slot Map of RandVar at rows of x.
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.
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.
signature(RandVar = "EuclRandVariable", distr = "Distribution"):
image distribution of distr under RandVar. Returns
an object of class "DistrList".
signature(object = "EuclRandVariable"):
dimension of the Euclidean random variable.
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".
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.
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.
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.
signature(x = "EuclRandVariable"):
Given a "Math" group generic fct, the Euclidean random
variable fct(x) is returned.
signature(object = "UnivariateDistribution", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under univariate distributions.
signature(object = "AbscontDistribution", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under absolutely continuous univariate distributions.
signature(object = "DiscreteDistribution", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under discrete univariate distributions.
signature(object = "MultivariateDistribution", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under multivariate distributions.
signature(object = "DiscreteMVDistribution", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under discrete multivariate distributions.
signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"):
conditional expectation of fun under conditional univariate distributions.
signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"):
conditional expectation of fun under absolutely continuous conditional univariate distributions.
signature(object = "UnivariateCondDistribution", fun = "EuclRandVariable", cond = "numeric"):
conditional expectation of fun under discrete conditional univariate distributions.
Matthias Kohl Matthias.Kohl@stamats.de
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.