The multivariate negative binomial-Lindley distribution. Properties and new representation for the univariate case

In this paper a multivariate negative binomial-Lindley distribution is introduced. The univariate version of this distribution comprises an alternative of the model proposed by Zamani and Ismail (2010). With respect to this latter model, this representation presents some advantages since it provides a tractable model with attractive properties that makes it suitable for application in any field where overdispersion is observed. Some properties of the model are studied including a recurrence for the probabilities of the multivariate and univariate distribution. An EM algorithm is derived to estimate the parameters of this multivariate distribution. Finally, some numerical applications for the univariate and bivariate cases are given to illustrate the performance of this model.