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

Author

Listed:
  • Subrata Chakraborty

    (Dibrugarh University)

  • Tomoaki Imoto

    (The Institute of Statistical Mathematics)

Abstract

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.

Suggested Citation

  • Subrata Chakraborty & Tomoaki Imoto, 2016. "Extended Conway-Maxwell-Poisson distribution and its properties and applications," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-19, December.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0044-1
    DOI: 10.1186/s40488-016-0044-1
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    References listed on IDEAS

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    1. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
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    Cited by:

    1. Boris Forthmann & Philipp Doebler, 2021. "Reliability of researcher capacity estimates and count data dispersion: a comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 3337-3354, April.
    2. Seng Huat Ong & Shin Zhu Sim & Shuangzhe Liu & Hari M. Srivastava, 2023. "A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data," Stats, MDPI, vol. 6(3), pages 1-14, September.
    3. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).

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