The Beta Product Distribution with Complex Parameters

Autor:	Daniel Dufresne
Rok vydání:	2010
Předmět:	Statistics and Probability Ratio distribution Beta negative binomial distribution Indecomposable distribution Infinite divisibility (probability) Generalized beta distribution Mathematical analysis Beta prime distribution Natural exponential family Product distribution Mathematics
Zdroj:	Communications in Statistics - Theory and Methods. 39:837-854
ISSN:	1532-415X 0361-0926
DOI:	10.1080/03610920902802599
Popis:	The family consisting of the distributions of products of two independent beta variables is extended to include cases where some of the parameters are not positive but negative or complex. This “beta product” distribution is expressible as a Meijer G function. An example (from risk theory) where such a distribution arises is given: an infinite sum of products of independent random variables is shown to have a distribution that is the product convolution of a complex-parameter beta product and an independent exponential. The distribution of the infinite sum is a new explicit solution of the stochastic equation X = (in law) B(X + C). Characterizations of some G distributions are also proved.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a1121aa8e3b90cf3004c0071e1325062 https://doi.org/10.1080/03610920902802599 Zobrazit plný text záznamu