SOME FORMS FOR $ r^{th}$ MOVING MAXIMA OF
ITERATED LOGARITHM LAW
Bader Almohaimeed
Department of Mathematics
College of Science
Qassim University
Buraydah 51431, P.O. Box 707, SAUDI ARABIA

Abstract

Let $ \eta_{r,n} $ be a sequence of independent random variables, which is identically distributed and is defined over common probability space $(\Omega,\cal{ F}, \cal{ A})$ for a continuous distribution function $F$. Let $ \eta_{r,n} $ denote the $ r^{th}$ upper order statistic between $(X_{n-a_{n}+1},X_{n-a_{n}+2},...,X_{n})$, for $n\geq 1$ with sequence $(a_{n})$ of integers, which is non-decreasing for $0\leq a_{n}\leq n$. In this paper, some forms of iterated logarithm law for $ \eta_{r,n} $ are obtained.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 5
Year: 2017

DOI: 10.12732/ijam.v30i5.7

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