On the Parameters Estimators for a Discrete Analog of the Generalized Exponential Distribution

Nekoukhou et. al (Commun. Statist. Th. Meth., 2012) introduced a two-parameters discrete probability distribution so-called Discrete Analog of the Generalized Exponential Distribution (in short, DGED). We shall attempt to derive conditions under which a solution for the system of likelihood equations exists and coincides with the maximum likelihood (ML) estimators of the DGED. This kind of ML estimators are coincided with some moment estimators. An approximate computation based on Fisher’s accumulation method is presented in order for the ML estimations of the unknown parameters. Simulation study is also illustrated. Meanwhile, in the sequel two special cases of the DGED are considered. Some statistical properties for such special cases of the DGED are provided. We also propose a linear regression-type model for estimation of the parameter. Finally, we fit the DGED to a real data set and compare it with two other discrete distributions.