D Family Dependent Random Variables, Random Weighting And The Tail Probability Of The Asymptotic Estimate

This paper deals with the approximation of the tail probability of randomly weighted sums of a sequence of pairwise asymptotically independent random variables with a common dominatedly-varying-tailed distribution function.The weights are independent of the former sequence, satisfying some assumptions about the moments.But no requirements on the depen-dence structure of the weights are imposed.