@article{EJP845,
author = {Daniel Dufresne},
title = {G distributions and the beta-gamma algebra},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {Beta distribution; beta product distribution; gamma distribution; G distributions; Barnes' lemmas; Mellin transforms; infinite divisibility; Macdonald's function},
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).},
pages = {no. 71, 2163-2199},
issn = {1083-6489},
doi = {10.1214/EJP.v15-845},
url = {http://ejp.ejpecp.org/article/view/845}}