REMARKS ON THOM'S ESTIMATORS FOR THE GAMMA DISTRIBUTION

L. R. SHENTON Computer Center, The University of Georgia, Athens, Ga.

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K. O. BOWMAN Computing Technology Center, Oak Ridge, Tenn.

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Abstract

Thom's estimators for the two-parameter gamma distribution arise as asymtotic approximations to the maximum likelihood estimators. Being perhaps the simplest estimators known in this case, their properties are here investigated. We show that although they do have slight asymptotic bias even in very large samples, yet for almost the whole of the parameter space they have smaller asymptotic variances than the maximum likelihood estimators; more than this there is evidence that in finite samples the property still holds. As for the type of the sampling distributions involved, Thom's estimators are in general slightly nearer to normality than the maximum likelihood estimators.

The occurrence of estimators that are improvements on the maximum likelihood estimators, be the improvement only slight, is rather rare and becomes of particular interest when they arise in a practical situation.

This work was partially supported through the Southeastern Forest Experiment Station with Department of Defense funds, IPR19-65-WEPS.

Part of this paper is based on work performed at the Computing Technology Center, operated by the Union Carbide Corporation, Nuclear Division, for the U.S. Atomic Energy Commission.

Abstract

Thom's estimators for the two-parameter gamma distribution arise as asymtotic approximations to the maximum likelihood estimators. Being perhaps the simplest estimators known in this case, their properties are here investigated. We show that although they do have slight asymptotic bias even in very large samples, yet for almost the whole of the parameter space they have smaller asymptotic variances than the maximum likelihood estimators; more than this there is evidence that in finite samples the property still holds. As for the type of the sampling distributions involved, Thom's estimators are in general slightly nearer to normality than the maximum likelihood estimators.

The occurrence of estimators that are improvements on the maximum likelihood estimators, be the improvement only slight, is rather rare and becomes of particular interest when they arise in a practical situation.

This work was partially supported through the Southeastern Forest Experiment Station with Department of Defense funds, IPR19-65-WEPS.

Part of this paper is based on work performed at the Computing Technology Center, operated by the Union Carbide Corporation, Nuclear Division, for the U.S. Atomic Energy Commission.

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