sn (version 0.4-3)

msn.affine: Affine transformation of a multivariate skew-normal or skew-t variable

Description

Computes the parameters of an affine transformation a+ A Y of a multivariate skew-normal or skew-t variable Y

Usage

msn.affine(dp, a=0, A, drop=TRUE)
  mst.affine(dp, a=0, A, drop=TRUE)

Arguments

dp

a list containg the pamaters of the variable being transformed; it must include components xi, Omega, alpha as described for dmsn; for mst.affine, also a component df

A

a matrix with ncol(A) equal to nrow(dp$Omega)

a

a vector wiht length(a) equal to nrow(dp$Omega)

drop

a logical flag (default value is TRUE) operating when nrow(A) equals 1. If these conditions are met, the output is provided in the form of parameters of a scalar distribution, dsn or dst, de

Value

• A list containing the same components of the input parameter dp

Background

For background information about the skew-normal and skew-t distributions, their parameters and the properties of affine transformations, see the references below. The specific formulae implemented by this function are given in Appendix A.2 of Capitanio et al.(2003).

References

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367--389.

Capitanio, A. et al. (2003). Graphical models for skew-normal variates. Scand. J. Statist. 30, 129--144.

See Also

dsn, dst, dmsn, dmst

Examples

dp<- list(xi=c(1,1,2), Omega=toeplitz(1/1:3), alpha=c(3,-1,2))
A <- matrix(c(1,-1,1,3,0,-2), 2, 3, byrow=TRUE) 
dp1 <- msn.affine(dp, 1:2, A)
#
dp$df <- 5
dp2<-  mst.affine(dp,,A[1,,drop=FALSE])
dp3<-  mst.affine(dp,,A[1,,drop=FALSE], drop=FALSE)
if(zapsmall(dp2$scale^2 - dp3$Omega)) print("something wrong here!")