Vasudeva, R. (2013) Almost sure behaviour of near moving maxima. Journal of Statistical Planning and Inference, 143 (1). 96 - 106.
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Let {X-n} be a sequence of independent and identically distributed random variables defined over a common probability space (Q,F,P) with common continuous distribution function F. Define eta(n) = max(n-an) < j <= (n)Xj(,) where a(n) is an integer with 0 < a(n) < n,n > 1. For any constant a > 0, let K-n((m))(a)=# {j,n-a(n) < j <= n,X-j is an element of (eta(n)-a, eta(n) )}> 1. Then K-n((m))(a) denotes the number of observations near moving maxima. In this paper, we obtain conditions for (K-n((m))(a)) to converge to 1 almost surely (a.s.), when a(n) ={n(p)}, and a(n) = pn],0 <p < 1,n >= 1. (C) 2012 Elsevier B.V.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Almost sure convergence, Near moving maxima, |
| Subjects: | E Mathematical Science > Statistics |
| Divisions: | Department of > Statistics |
| Depositing User: | Arshiya Kousar Library Assistant |
| Date Deposited: | 18 Dec 2019 10:18 |
| Last Modified: | 18 Dec 2019 10:18 |
| URI: | http://eprints.uni-mysore.ac.in/id/eprint/10272 |
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