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Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution

Author

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  • Dai, Hongsheng
  • Bao, Yanchun
  • Bao, Mingtang

Abstract

This paper shows that the maximum likelihood estimate (MLE) for the dispersion parameter of the negative binomial distribution is unique under a certain condition. A fixed-point iteration algorithm is proposed and it guarantees to converge to the MLE, when the score function has a unique root.

Suggested Citation

  • Dai, Hongsheng & Bao, Yanchun & Bao, Mingtang, 2013. "Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 21-27.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:21-27
    DOI: 10.1016/j.spl.2012.08.017
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    References listed on IDEAS

    as
    1. L. Willson & J. Folks & J. Young, 1986. "Complete sufficiency and maximum likelihood estimation for the two-parameter negative binomial distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 33(1), pages 349-362, December.
    2. Kuan, Pei Fen & Chung, Dongjun & Pan, Guangjin & Thomson, James A. & Stewart, Ron & Keleş, Sündüz, 2011. "A Statistical Framework for the Analysis of ChIP-Seq Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 891-903.
    3. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
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    Citations

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    Cited by:

    1. Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2021. "Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations," Papers 2110.03552, arXiv.org, revised Feb 2022.
    2. Bandara, Udika & Gill, Ryan & Mitra, Riten, 2019. "On computing maximum likelihood estimates for the negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 54-58.
    3. Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2022. "Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations," Mathematics, MDPI, vol. 10(10), pages 1-25, May.

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