affineTransSECdistr: 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)

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.

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.

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.

Examples

Run this code

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")

Run the code above in your browser using DataLab

Last chance! 50% off unlimited learning