A COM-Poisson-type generalization of the negative binomial distribution

This paper introduces a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution. Many well-known distributions are particular and limiting distributions. The proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-Poisson distributions. Probability and moment recurrence formulae, and probabilistic and reliability properties have been derived. With the flexibility to model under-, equi- and over-dispersion, and its various interesting properties, this NB generalization will be a useful model for count data. An application to empirical modeling is illustrated with a real data set.