Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1153173 | Statistics & Probability Letters | 2013 | 9 Pages |
Abstract
For a sequence {Xn,nâ¥1} of random variables, set Yn=max1â¤kâ¤nXkâan, where {an,nâ¥1} is a sequence of constants to be specified. We obtain the limiting behavior of the sequences of positive and negative parts of {Yn,nâ¥1} when the tail distribution of {Xn,nâ¥1} satisfies suitable “exponential-type” conditions. Next, we consider the rate convergence of the positive part to zero (results similar to complete convergence).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Rita Giuliano Antonini, Thuntida Ngamkham, Andrei Volodin,