A New Bivariate Distribution Obtained by Compounding the Bivariate Normal and Geometric Distributions

Abstract

Recently, Mahmoudi and Mahmoodian [7] introduced a new class of distributions which contains univariate normal–geometric distribution as a special case. This class of distributions are very flexible and can be used quite effectively to analyze skewed data. In this paper we propose a new bivariate distribution with the normal–geometric distribution marginals. Different properties of this new bivariate distribution have been studied. This distribution has five unknown parameters. The EM algorithm is used to determine the maximum likelihood estimates of the parameters. We analyze one series of real data set for illustrative purposes.

Keywords

• Normal distribution; Geometric distribution; EM algorithm; Maximum likelihood estimation.