Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables

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. Whe...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2012, Vol.52 (1), p.29-39
Main Authors: Cheng, Dongya, Wang, Yuebao
Format: Article
Language:English
Subjects:
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-012-9153-9