Uniform asymptotics for the tail probability of weighted sums with heavy tails

被引:2
|
作者
Zhang, Chenhua [1 ]
机构
[1] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA
关键词
Uniform long-tailedness; Long-tailed distribution; h-insensitive function; Dominated variation; Quasi-asymptotical independence; INDEPENDENT RANDOM-VARIABLES; MAXIMUM;
D O I
10.1016/j.spl.2014.07.022
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper studies the tail probability of weighted sums of the form Sigma(n)(i=1) c(i)X(i), where random variables Xi's are either independent or pairwise quasi-asymptotically independent with heavy tails. Using the idea of uniform long-tailedness, the uniform asymptotic equivalence of the tail probabilities of Sigma(n)(i=1) c(i)X(i), max(1 <= k <= n) Sigma(k)(i=1) c(i)X(i) and Sigma(n)(i=1) c(i)X(i)(+) is established, where Xi's are independent and follow the long-tailed distribution, and c(i)'s take value in a broad interval. Some further uniform asymptotic results for the weighted sums of X's with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码:221 / 229
页数:9
相关论文
共 50 条