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Quasi-negative binomial distribution: Properties and applications

Author

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  • Li, Shubiao
  • Yang, Fang
  • Famoye, Felix
  • Lee, Carl
  • Black, Dennis

Abstract

In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.

Suggested Citation

  • Li, Shubiao & Yang, Fang & Famoye, Felix & Lee, Carl & Black, Dennis, 2011. "Quasi-negative binomial distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2363-2371, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2363-2371
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    References listed on IDEAS

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    1. P.C. Consul & F. Famoye, 1986. "On The Unimodality Of Generalized Poisson Distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(2), pages 117-122, June.
    2. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    3. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
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    Cited by:

    1. Jamiu S. Olumoh & Osho O. Ajayi & Sauta S. AbdulKadir, 2022. "A quasi-negative binomial regression with an application to medical care data," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(5), pages 3029-3052, October.
    2. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.

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