A Bivariate Discrete Lindley Distribution and Applications

In this paper a bivariate discrete Lindley distribution has been derived from a discrete Lindely distribution using Farlie-Gumbel-Morgenstern copula. Some properties of this distribution such as probability generating function, conditional distributions, Pearson's correlation andreliability parameter are studied. To estimate the parameters of the distribution, three methods of estimation were presented. Method of moments, maximum likelihood estimation and two-step maximum likelihood. Finally, simulation study and a practical application were made on real data to show the appropriateness of the proposed distribution on these data.