# Euclidean random variable Class of Euclidean random variables. class ## 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 ```r 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) ```

EuclRandVariable-class function