Tail Behaviour of Weighted Sums of Order Statistics of Dependent Risks

2014/08/06 by Hashorva, Enkelejd, Li, Jinzhi
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1408.1296

Abstract

Let X₁,… ,X_n be n real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics X_1:n≤ ⋯ ≤ X_n:n of X₁,… ,X_n under the general case in which the distribution function of X_n:n is long-tailed or rapidly varying and % X₁,… ,X_n may not be comparable in terms of their tail probability. We also present two examples and an application of our results in risk theory.

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