Randomly weighted sums of linearly wide quadrant-dependent random variables with heavy tails

Changjun Yu and Dongya Cheng

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 2, 591-601

Abstract: This paper investigates tail behavior of the randomly weighted sum ∑nk = 1θkXk and reaches an asymptotic formula, where Xk, 1 ⩽ k ⩽ n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θk, 1 ⩽ k ⩽ n, independent of Xk, 1 ⩽ k ⩽ n, are n non-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones.

Date: 2017
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DOI: 10.1080/03610926.2014.1000500

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