Acta Mathematica Sinica-English series, ( ISI ), Volume (29), No (2), Year (2013-2) , Pages (355-364)
Title : ( Asymptotic behavior of product of two heavy-tailed Dependent Random Variables )
Authors: Vahid Ranjbar , Mohammad Amini , Jaap Geluk , Abolghasem Bozorgnia ,
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Abstract
Let emph{X} and emph{Y} be positive weakly negatively dependent (WND) random variables with finite expectations and continuous distribution functions emph{F} and emph{G } with heavy tails, respectively. The asymptotic behavior of the tail of distribution of emph{XY} is studied and some closure properties under some suitable conditions o bar{F}(x)=1-F(x) and bar{G}(x)=1-G(x) are provided. Moreover, Subexponentiality of XY when X and Y are WND random variables is derived.
