G distributions and the beta-gamma algebra

被引：20
作者：
Dufresne, Daniel [1 ]
机构：
[1] Univ Melbourne, Ctr Actuarial Studies, Melbourne, Vic 3010, Australia
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷
关键词：
Beta distribution; beta product distribution; gamma distribution; G distributions; Barnes' lemmas; Mellin transforms; infinite divisibility; Macdonald's function;
D O I：
10.1214/EJP.v15-845
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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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页码：2163 / 2199
页数：37
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