Geometric Skew Normal Distribution

In this article, we introduce a new three-parameter skewed distribution of which normal distribution is a special case. This distribution is obtained by using geometric sum of independent identically distributed normal random variables. We call this distribution as the geometric skew normal distribution. Different properties of this new distribution have been investigated. The probability density function of geometric skew normal distribution can be unimodal or multimodal, and it always has an increasing hazard rate function. It is an infinite divisible distribution, and it can have heavier tails. The maximum likelihood estimators cannot be obtained in explicit forms. The EM algorithm has been proposed to compute the maximum likelihood estimators of the unknown parameters. One data analysis has been performed for illustrative purposes. We further consider multivariate geometric skew normal distribution and explore its different properties. The proposed multivariate model induces a multivariate Levy process, and some properties of this multivariate process have been investigated. Finally, we conclude the paper.