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A COM–Poisson type generalization of the binomial distribution and its properties and applications

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  • Borges, Patrick
  • Rodrigues, Josemar
  • Balakrishnan, Narayanaswamy
  • Bazán, Jorge

Abstract

Shmueli et al. (2005) introduced the COM–Poisson–binomial distribution, but they did not study the mathematical properties of this family of distributions. In this paper, we discuss some properties and an asymptotic approximation of it by the COM–Poisson distribution. Moreover, three datasets are also considered.

Suggested Citation

  • Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:158-166
    DOI: 10.1016/j.spl.2014.01.019
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    References listed on IDEAS

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    1. Ramesh Gupta & Hui Tao, 2010. "A generalized correlated binomial distribution with application in multiple testing problems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 59-77, January.
    2. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy, 2012. "Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1703-1713.
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    4. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
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    8. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    9. Chen-An Tsai & Huey-miin Hsueh & James J. Chen, 2003. "Estimation of False Discovery Rates in Multiple Testing: Application to Gene Microarray Data," Biometrics, The International Biometric Society, vol. 59(4), pages 1071-1081, December.
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    Cited by:

    1. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    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. Morris, Darcy Steeg & Raim, Andrew M. & Sellers, Kimberly F., 2020. "A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    4. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.
    5. Rodrigues, Josemar & Bazán, Jorge L. & Suzuki, Adriano K. & Balakrishnan, Narayanaswamy, 2016. "The Bayesian restricted Conway–Maxwell-Binomial model to control dispersion in count data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 281-288.

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