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G distributions and the beta-gamma algebra


 
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1. Title Title of document G distributions and the beta-gamma algebra
 
2. Creator Author's name, affiliation, country Daniel Dufresne; University of Melbourne; Australia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Beta distribution; beta product distribution; gamma distribution; G distributions; Barnes' lemmas; Mellin transforms; infinite divisibility; Macdonald's function
 
3. Subject Subject classification 97K60; 65R10; 60E07; 33B15
 
4. Description 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).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-12-15
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/845
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-845
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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