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Runs in an ordered sequence of random variables

Authors:	Serkan Eryılmaz Alexei Stepanov

Institution:	(1) Department of Mathematics, Izmir University of Economics, Sakarya Caddesi No. 156, 35330 Balcova, Izmir, Turkey;(2) Department of Mathematics, Kaliningrad State Technical University, Sovietsky Prospect 1, Kaliningrad, 236000, Russia

Abstract:	Let $X_{1},\ldots,X_{n}$ be independent and identically distributed random variables with continuous distribution function. Denote by $X_{1:n} \leq \cdots \leq X_{n:n}$ the corresponding order statistics. In the present paper, the concept of $\varepsilon$ -neighbourhood runs, which is an extension of the usual run concept to the continuous case, is developed for the sequence of ordered random variables $X_{1:n}\leq\cdots\leq X_{n:n}.$

Keywords:	Asymptotic results Dispersion Exchangeable random variables Order statistics Spacings Runs Longest run
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