# Multivariate Geometric Skew-Normal Distribution

## TL;DR

This paper introduces the multivariate geometric skew-normal distribution, explores its properties, and demonstrates its advantages and ease of use through simulations and real data analysis.

## Contribution

It extends the geometric skew-normal distribution to multivariate cases, providing new properties, characterization results, and an EM algorithm for parameter estimation.

## Key findings

- The distribution can take various shapes in its joint density.
- The EM algorithm performs well in parameter estimation.
- The model fits real data effectively.

## Abstract

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.