Tail behavior of negatively associated heavy-tailed sums
2006 ◽
Vol 43
(2)
◽
pp. 587-593
◽
Keyword(s):
Class D
◽
Consider a sequence {Xk, k ≥ 1} of random variables on (−∞, ∞). Results on the asymptotic tail probabilities of the quantities , and S(n) = max0 ≤ k ≤ nSk, with X0 = 0 and n ≥ 1, are well known in the case where the random variables are independent with a heavy-tailed (subexponential) distribution. In this paper we investigate the validity of these results under more general assumptions. We consider extensions under the assumptions of having long-tailed distributions (the class L) and having the class D ∩ L, where D is the class of distribution functions with dominatedly varying tails. Some results are also given in the case where Xk, k ≥ 1, are not necessarily identically distributed and/or independent.
2006 ◽
Vol 43
(02)
◽
pp. 587-593
◽
2008 ◽
Vol 45
(1)
◽
pp. 85-94
◽
2005 ◽
Vol 42
(2)
◽
pp. 426-445
◽
2008 ◽
Vol 45
(01)
◽
pp. 85-94
◽
2015 ◽
Vol 44
(1)
◽
pp. 12-27
◽
2008 ◽
Vol 22
(4)
◽
pp. 871-882
◽
2018 ◽
Vol 164
◽
pp. 40-53
◽
Keyword(s):
2009 ◽
Vol 46
(2)
◽
pp. 559-570
◽