Document Type

Article

Publication Date

1-1-2014

School

Mathematics and Natural Sciences

Abstract

This paper studies the tail probability of weighted sums of the form ∑i=1nciXi, where random variables X i'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 ∑i=1nciXi, max1≤k≤n∑i=1kciXi and ∑i=1nciXi+ is established, where X i'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 i's with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented. © 2014 Elsevier B.V.

Comments

© 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/.

Publication Title

Statistics and Probability Letters

Volume

94

First Page

221

Last Page

229

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