Title: Univariate and Bivariate Geometric Discrete Generalized Exponential Distributions,
Abstract: Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very
powerful method to introduce an additional parameter to a class of continuous
distribution functions and hence it brings more flexibility to the model. They
have demonstrated their method for the exponential and Weibull classes. In the
same paper they have briefly indicated regarding its bivariate extension. The
main aim of this paper is to introduce the same method, for the first time, to
the class of discrete generalized exponential distributions both for the
univariate and bivariate cases. We investigate several properties of the
proposed univariate and bivariate classes. The univariate class has three
parameters, whereas the bivariate class has five parameters. It is observed
that depending on the parameter values the univariate class can be both zero
inflated as well as heavy tailed. We propose to use EM algorithm to estimate
the unknown parameters. Small simulation experiments have been performed to see
the effectiveness of the proposed EM algorithm, and a bivariate data set has
been analyzed and it is observed that the proposed models and the EM algorithm
work quite well in practice.