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On estimation of the shape parameter of the gamma distribution

Author

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  • Zaigraev, A.
  • Podraza-Karakulska, A.

Abstract

The problem of estimation of an unknown shape parameter under the sample drawn from the gamma distribution, where the scale parameter is also unknown, is considered. A new estimator, called the maximum likelihood scale invariant estimator, is proposed. It is established that both the bias and the variance of this estimator are less than that of the usual maximum likelihood estimator. A property of the psi function is also obtained.

Suggested Citation

  • Zaigraev, A. & Podraza-Karakulska, A., 2008. "On estimation of the shape parameter of the gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 286-295, February.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:3:p:286-295
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    Cited by:

    1. Takagi, Yoshiji, 2012. "On the estimation of the shape parameter of the gamma distribution in second-order asymptotics," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 15-21.
    2. Zaigraev, A. & Podraza-Karakulska, A., 2014. "Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 99-106.
    3. Haitian Xie, 2020. "Finite-Sample Average Bid Auction," Papers 2008.10217, arXiv.org, revised Feb 2022.

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