R: Affine transformations and marginals of a skew-elliptical...

affineTransSECdistr {sn} | R Documentation

## Affine transformations and marginals of a skew-elliptical distribution

### Description

Given a multivariate random variable Y with skew-elliptical (SEC) distribution, compute the distribution of a (possibly multivariate) marginal or the distribution of an affine transformation a + A'Y.

### Usage

      affineTransSECdistr(object, a, A, name, compNames, drop=TRUE)
      marginalSECdistr(object, comp, name, drop=TRUE)

### Arguments

`object` | an object of class `SECdistrMv` which identifies the source random variable, as created by `makeSECdistr` or by `extractSECdistr` or by a previous call to these functions
`a` | a numeric vector with the length `ncol(A)`.
`A` | a full-rank matrix with `nrow(A)` equal to the dimensionality `d` of the random variable identified by `object`.
`name` | an optional character string representing the name of the outcome distribution; if missing, one such string is constructed.
`compNames` | an optional vector of length `ncol(A)` of character strings with the names of the components of the outcome distribution; if missing, one such vector is constructed.
`drop` | a logical flag (default value: `TRUE`), operating only if the returned object has dimension `d=1`, in which case it indicates whether this object must be of class `SECdistrUv`.
`comp` | a vector formed by a subset of `1:d` which indicates which components must be extracted from `object`, on denoting by `d` its dimensionality.

### Value

If `object` defines the distribution of a SEC random variable Y, `affineTransSECdistr` computes the distribution of a+A'Y and `marginalSECdistr` computes the marginal distribution of the `comp` components. In both cases the returned object is of class `SECdistrMv`, except when `drop=TRUE` operates, leading to an object of class `SECdistrUv`.

### Background

These functions implement formulae given in Sections 5.1.4, 5.1.6 and 6.2.2 of the reference below.

### References

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.

### See Also

`makeSECdistr`, `extractSECdistr`, `SECdistrMv-class`

### Examples

    dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(3,-1,2), nu=5)
    st3 <- makeSECdistr(dp3, family="ST", name="ST3", compNames=c("U", "V", "W"))
    A <- matrix(c(1,-1,1, 3,0,-2), 3, 2)
    new.st <- affineTransSECdistr(st3, a=c(-3,0), A=A)
    #
    st2 <- marginalSECdistr(st3, comp=c(3,1), name="2D marginal of ST3")

[Package sn version 1.5-3 Index]