Additive properties of skew normal random vectors

We show that for a random vector with a multivariate closed skew normal (CSN) distribution all column (row) full rank linear transformations are in the family of CSN distributions. We also show the closure of sums of independent CSN random vectors and provide a characterization for the CSN. We consider alternative representations of multivariate skew normal distributions as particular cases of the CSN and use some of them to illustrate the above properties. (C) 2003 Elsevier B.V. All rights reserved.