G distributions and the beta-gamma algebra

Daniel Dufresne (University of Melbourne)

Abstract


This paper has four interrelated themes: (1) express Laplace and Mellin transforms of sums of positive random variables in terms of the Mellin transform of the summands; (2) show the equivalence of the two Barnes' lemmas with known properties of gamma distributions; (3) establish properties of the sum of two reciprocal gamma variables, and related results; (4) study the G distributions (whose Mellin transforms are ratios of products of gamma functions).

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Pages: 2163-2199

Publication Date: December 15, 2010

DOI: 10.1214/EJP.v15-845

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