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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0908.

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Length: 19 pages
Date of creation: 23 Sep 2009
Date of revision:
Handle: RePEc:vic:vicewp:0908

Note: ISSN 1485-6441
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Keywords: Maximum likelihood estimator; bias reduction; gamma distribution;

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  1. David E. Giles & Hui Feng & Ryan T. Godwin, 2011. "Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution," Econometrics Working Papers 1105, Department of Economics, University of Victoria.
  2. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
  3. 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.
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