Inflated-Parameter Negative Binomial and Poisson Distributions;

In Practical situations, the necessity of using a richer class of the classic discrete probability distributions, such as the negative binomial and Poisson distributions, is felt. In this article, by entering an additional parameter ρ, we extend these classic distributions to the class of inflated-parameter distributions. We show that these generalized distributions are suitable in modeling correlated count data with superdispersion. In particular, we illustrate this by applying them to some set of real data concerning number of claims in an insurance company. Finally, important characteristics of these distributions are compared with those of the corresponding classic distributions.