To cite this version:A. Zaigraev, A. Podraza-Karakulska. On estimation of the shape parameter of the gamma distribution. Statistics and Probability Letters, Elsevier, 2009, 78 (3) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p tOn estimation of the shape parameter of the gamma distribution A. Zaigraev * and A. Podraza-Karakulska Nicolaus Copernicus University of Toruń AbstractThe 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.

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Abstract. The maximum likelihood scale invariant estimator of the shape parameter of the gamma distribution, proposed by the authors [Statist. Probab. Lett. 78 (2008)], is considered. The asymptotics of the mean square error of this estimator, with respect to that of the usual maximum likelihood estimator, is established.