Description Objects from the Class Slots Extends Methods Author(s) See Also Examples

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`

.

`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.

Class `"RandVariable"`

, directly.

- 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.

Matthias Kohl [email protected]

`EuclRandVariable`

, `RandVariable-class`

,
`EuclRandMatrix-class`

, `EuclRandVarList-class`

,
`Distribution-class`

, `Arith`

,
`Math`

, `E`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
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)
``` |

RandVar documentation built on May 2, 2019, 5:20 p.m.

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