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A class of probability distributions that is closed with respect to addition as well as multiplication of independent random variablesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 28, no 3, 1063-1081 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2015. Vol. 28, no 3, 1063-1081 p.
##### Keyword [en]

Generalized gamma convolution, generalized negative binomial convolution, hyperbolic complete monotonicity, infinite divisibility, self-decomposability
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:umu:diva-85052DOI: 10.1007/s10959-013-0523-yOAI: oai:DiVA.org:umu-85052DiVA: diva2:691346
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Available from: 2014-01-27 Created: 2014-01-27 Last updated: 2015-11-16Bibliographically approved

Thorin’s class of generalized gamma convolutions (GGCs) is closed with respect to change in scale, weak limits, and addition of independent random variables. Here, it is shown that the GGC class also has the remarkable property of being closed with respect to multiplication of independent random variables. This novel result, which has a simple extension to symmetric distributions on R, has many consequences and applications. In particular, it follows that X∼ GGC implies that exp(X)∼ GGC. The latter result is used to find a large class of explicit probability functions on {0,1,2,…} which are generalized negative binomial convolutions (GNBCs). The paper ends with several open problems.

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