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Bias of the Maximum Likelihood Estimators of the Two-Parameter Gamma Distribution Revisited

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Abstract

We consider the quality of the maximum likelihood estimators for the parameters of the two-parameter gamma distribution in small samples. We show that the methodology suggested by Cox and Snell (1968) can be used very easily to bias-adjust these estimators. A simulation study shows that this analytic correction is frequently much more effective than bias-adjusting using the bootstrap – generally by an order of magnitude in percentage terms. The two bias-correction methods considered result in increased variability in small samples, and the original estimators and their bias-corrected counterparts all have similar percentage mean squared errors.

Suggested Citation

  • David E. Giles & Hui Feng, 2009. "Bias of the Maximum Likelihood Estimators of the Two-Parameter Gamma Distribution Revisited," Econometrics Working Papers 0908, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0908
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0908.pdf
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    References listed on IDEAS

    as
    1. David E. Giles & Hui Feng & Ryan T. Godwin, 2016. "Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2465-2483, April.
    2. David E. Giles, 2009. "Bias Reduction for the Maximum Likelihood Estimator of the Scale Parameter in the Half-Logistic Distribution," Econometrics Working Papers 0901, Department of Economics, University of Victoria.
    3. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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    Cited by:

    1. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

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    More about this item

    Keywords

    Maximum likelihood estimator; bias reduction; gamma distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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