Extended Conway-Maxwell-Poisson distribution and its properties and applications

A new four parameter extended Conway-Maxwell-Poisson (ECOMP) distribution which unifies 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] is proposed. The additional parameter allows this distribution to have longer (shorter) tail compared to COM-NB and GCOMP. The proposed distribution can be formulated as an exponential combination of negative binomial and COM-Poisson distribution and also arises from a queuing system with state dependent arrival and service rates and belongs to exponential family when one of the parameter is considered as nuisance. Important distributional, reliability and stochastic ordering properties along with asymptotic approximations for the normalizing constant and the mean of this distribution is investigated. Method of parameter estimation and three comparative data fitting applications are also discussed.