  Azzalini (1985) introduced a skew-normal distribution of which normal
distribution is a special case. Recently Kundu (2014) introduced a geometric
skew-normal distribution and showed that it has certain advantages over
Azzalini's skew-normal distribution. In this paper we discuss about the
multivariate geometric skew-normal distribution. It can be used as an
alternative to Azzalini's skew normal distribution. We discuss different
properties of the proposed distribution. It is observed that the joint
probability density function of the multivariate geometric skew normal
distribution can take variety of shapes. Several characterization results have
been established. Generation from a multivariate geometric skew normal
distribution is quite simple, hence the simulation experiments can be performed
quite easily. The maximum likelihood estimators of the unknown parameters can
be obtained quite conveniently using expectation maximization (EM) algorithm.
We perform some simulation experiments and it is observed that the performances
of the proposed EM algorithm are quite satisfactory. Further, the analyses of
two data sets have been performed, and it is observed that the proposed methods
and the model work very well.
