On Beta-Product Convolutions

Details On Beta-Product Convolutions On Beta-Product Convolutions

2010-01-26

arxiv.org/abs/1001.4684v3

Mathematics

Probability

12 pages

Scientific paper

Let R be a positive random variable independent of S which is beta distributed. In this paper we are interested on the relation between the distribution function of R and that of RS. For this model we derive first some distributional properties, and then investigate the lower tail asymptotics of RS when R is regularly varying at 0, and vice-versa. Our first application concerns the asymptotic behaviour of the componentwise sample minima related to an elliptical distributions. Further, we derive the lower tails asymptotic of the aggregated risk for bivariate polar distributions.

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