Approximation of the Tail Probabilities of Randomly Weighted Sums in Presence of Dependence and Heavy Tails

Let {X_k; k ≥ 1} be a sequence of real-valued random variables and {θk; k ≥ 1} be other n random variables which are independent of the form sequence. Suppose that {X_k; k ≥ 1} are pairwise generalized negatively orthant dependent with heavy tails under the condition that {θ_k; k ≥ 1} are independent or associated, some asymptotic formulas are established.