The Positive Negative Binomial-Lindley Distribution and Its Applications

In this paper, the positive negative binomial-Lindley distribution is used to model count data for which the value zero cannot occur, which means that the NB-L distribution has to be adjusted for the missing zeros. We introduce and investigate some characteristics of the proposed distributions, such as the mean and variance. For the simulation, the parameters of the proposed distributions are estimated based on the maximum likelihood estimation method. We consider the efficiency of this parameter estimation method based on the mean squared error. It is applied in two applications; the positive NB-L distribution provides a better fit than the zero-truncated Poisson and the zero-truncated Poisson-Lindley distributions.