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The exact density of a statistic related to the shape parameter of a gamma variate

Authors:	S B Provost

Institution:	(1) Department of Statistical and Actuarial Sciences, The University of Western Ontario, N6A 5B9 London, Ontario, Canada

Abstract:	The exact density of the statistic ln $\bar x/\tilde x$ , where $\bar x$ and $\tilde x$ denote, respectively, the arithmetic and the geometric means of a random sample from a two-parameter gamma distribution, is obtained in a computable form using the technique of the inverse Mellin transform. This statistic is related to the maximum likelihood estimator of the shape parameter of a gamma distribution.

Keywords:	Exact density gamma distribution parametric inference Mellin transform
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