Extension of a negative multinomial model

An extension and applications of a negative multinomial model are presented. Unification of this and other models is studied. The extended model is shown to be the product of a negative multinomial distribution and a multinomial distribution such that the joint distribution has its “success” probabilities adding up to one. Among other properties, this discrete multivariate distribution provides a natural extension to the inverse sampling scheme and is also the limiting distribution of another related practical model. The maximum likelihood estimator and the UMVUE of the parameters are also determined.