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.