  A new three parameter natural extension of the Conway-Maxwell-Poisson
(COM-Poisson) distribution is proposed. This distribution includes the recently
proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty,
S. and Ong, S. H. (2014): A COM-type Generalization of the Negative Binomial
Distribution, Accepted in Communications in Statistics-Theory and Methods] and
the generalized COM-Poisson (GCOMP) distribution [Imoto, T. :(2014) A
generalized Conway-Maxwell-Poisson distribution which includes the negative
binomial distribution, Applied Mathematics and Computation, 247, 824-834]. The
proposed distribution is derived from a queuing system with state dependent
arrival and service rates and also from an exponential combination of negative
binomial and COM-Poisson distribution. Some distributional, reliability and
stochastic ordering properties are investigated. Computational asymptotic
approximations, different characterizations, parameter estimation and data
fitting example also discussed.
