Abstract
For a fixed integer n ≥ 2, let X 1 ,…, X n be independent random variables (r.v.s) with distributions F 1,…,F n , respectively. Let Y be another random variable with distribution G belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each tail of F i , i = 1,…,n, is asymptotically less than or equal to the tail of G, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum X 1 + ⋯ + X n and Y. By taking different G’s, we obtain general forms of some existing results.
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Research supported by the National Science Foundation of China (No. 11071182).
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Cheng, D., Wang, Y. Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables. Lith Math J 52, 29–39 (2012). https://doi.org/10.1007/s10986-012-9153-9
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DOI: https://doi.org/10.1007/s10986-012-9153-9