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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

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    1. 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.
    2. 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.
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