Article ID Journal Published Year Pages File Type
1144987 Journal of the Korean Statistical Society 2010 10 Pages PDF
Abstract

This paper achieves some weakly asymptotic formulas of the tail probability of randomly weighted sums ∑i=1nΘiXi and their maxima, where {Xi,i≥1}{Xi,i≥1} are bivariate upper tail independent random variables with common distribution FF belonging to the dominant variation class, and {Θi,i≥1}{Θi,i≥1} are other nonnegative random variables and independent of {Xi,i≥1}{Xi,i≥1}. Particularly, when FF belongs to the consistent variation class, some asymptotic formulas are established. An application to risk theory is proposed. The obtained results extend and improve the existing results of Zhang, Shen, and Weng (2009).

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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