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

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  • Zhang, Chenhua

Abstract

This paper studies the tail probability of weighted sums of the form ∑i=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 ∑i=1nciXi, max1≤k≤n∑i=1kciXi and ∑i=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.

Suggested Citation

  • Zhang, Chenhua, 2014. "Uniform asymptotics for the tail probability of weighted sums with heavy tails," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 221-229.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:221-229
    DOI: 10.1016/j.spl.2014.07.022
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    References listed on IDEAS

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