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A class of scale mixtures of Gamma(k)-distributions that are generalized gamma convolutions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, no 1, 773-787 p.Article in journal (Refereed) Published
Abstract [en]

Let k > 0 be an integer and Y a standard Gamma(k) distributed random variable. Let X be an independent positive random variable with a density that is hyperbolically monotone (HIM) of order k. Then Y . X and Y/X both have distributions that are generalized gamma convolutions (GGCs). This result extends a result of Roynette et al. from 2009 who treated the case k = 1 but without use of the HM-concept. Applications in excursion theory of diffusions and in the theory of exponential functionals of Levy processes are mentioned.

Place, publisher, year, edition, pages
2017. Vol. 23, no 1, 773-787 p.
Keyword [en]
excursion theory, exponential functionals, generalized gamma convolution, hyperbolic monotonicity, Levy process, products and ratios of independent random variables
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-130215DOI: 10.3150/15-BEJ761ISI: 000389565500029OAI: oai:DiVA.org:umu-130215DiVA: diva2:1070983
Available from: 2017-02-02 Created: 2017-01-14 Last updated: 2017-02-02Bibliographically approved

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