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

Chenhua Zhang

Statistics & Probability Letters, 2014, vol. 94, issue C, 221-229

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.

Keywords: Uniform long-tailedness; Long-tailed distribution; h-insensitive function; Dominated variation; Quasi-asymptotical independence (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.07.022

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