Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1151740 | Statistics & Probability Letters | 2014 | 9 Pages |
Abstract
This paper studies the tail probability of weighted sums of the form âi=1nciXi, 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 âi=1nciXi, max1â¤kâ¤nâi=1kciXi and âi=1nciXi+ is established, where Xi's are independent and follow the long-tailed distribution, and ci's take value in a broad interval. Some further uniform asymptotic results for the weighted sums of Xi's with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Chenhua Zhang,