Abstract
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.
Highlights
Two new generalizations of the well known COM-Poisson (Conway and Maxwell 1962) was proposed
In the present article we propose a natural four parameter extension of the COM-Poisson distribution which includes the recently introduced COM-Poisson type negative binomial (COM-NB) and GCOM-Poisson distributions as special cases
2 Extended COM-Poisson (ECOMP) distribution Here we introduce a new distribution that unifies both the COM-NB and generalized COM-Poisson (GCOMP) distributions
Summary
Two new generalizations of the well known COM-Poisson (Conway and Maxwell 1962) was proposed. In the present article we propose a natural four parameter extension of the COM-Poisson distribution which includes the recently introduced COM-NB and GCOM-Poisson distributions as special cases. This new distribution with additional parameters is more flexible in terms of tail length and dispersion index. Particular cases: The ECOMP (ν, p, α, β) distribution reduces to COM-NB (ν, p, α) for β = 1, to GCOMP (ν, p, β) for α = 1, to COMP (p, α − β) for ν = 1, to COMP (p, α) for β = 0, to Poisson (p) for ν = 1, α = β + 1, to Poisson (p) for β = 0, α = 1, to NB (ν, p) for α = β = 1 and to a new generalization of NB(NGNB) distribution when α = β = γ with pmf ν þ k k−1 γ pk =1Syy ð7Þ. 2.1 Shape of the pmf It is observed from the plots of the pmf of the ECOMP(v, p, α, β) distribution for different values of the parameters in Fig. 1, that the distribution is very flexible and can be non increasing with mode at zero, unique non zero mode, two modes and bimodal with one mode always at zero
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