Multivariate geometric skew-normal distribution

ABSTRACT

Azzalini [A class of distributions which include the normal. Scand J Stat. 1985;12:171–178] introduced a skew-normal distribution of which normal distribution is a special case. Recently, Kundu [Geometric skew normal distribution. Sankhya Ser B. 2014;76:167–189] 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 (MGSN) 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 MGSN distribution can take a variety of shapes. Several characterization results have been established. Generation from an MGSN 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 the expectation–maximization (EM) algorithm. We perform some simulation experiments and it is observed that the performances of the proposed EM algorithm are quite satisfactory. Furthermore, the analyses of two data sets have been performed, and it is observed that the proposed methods and the model work very well.

KEYWORDS:

• Skew-normal distribution
• moment-generating function
• infinite divisible distribution
• maximum likelihood estimators
• EM algorithm
• Fisher information matrix

AMS 2000 SUBJECT CLASSIFICATION:

• Primary: 62F10
• Secondary: 62H10

Acknowledgments

The author would like to thank Prof. Dimitris Karlis from the Athens University of Economics and Business, Greece, for his helpful comments. The author is really thankful to two reviewers and the associate editor for their careful reading and providing constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author.