Inflated-Parameter Family of Generalized Power Series Distributions And Their Application In Analysis Of Over dispersed Insurance Data

In this paper we suggest an extension of tile generalized power series distributions by including an additional parameter p. It has a natural interpretation in terms of both "zeroinflated" proportion and correlation coefficient. A new concept of p-type lack of memory property is introduced. The proposed new discrete distributions are candidates for modeling of correlated count data which exhibit overdispersion. Two alternative representations of the probability mass flmctions of the extended distributions are given. A real frequency data are fitted successfully with the extended Poisson and negative binomial models.