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Runs in an ordered sequence of random variables

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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 \(X_{1:n}\leq\cdots\leq X_{n:n}.\)

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Authors and Affiliations

  1. Department of Mathematics, Izmir University of Economics, Sakarya Caddesi No. 156, 35330, Balcova, Izmir, Turkey

    Serkan Eryılmaz

  2. Department of Mathematics, Kaliningrad State Technical University, Sovietsky Prospect 1, Kaliningrad, 236000, Russia

    Alexei Stepanov

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  1. Serkan Eryılmaz
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  2. Alexei Stepanov
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Correspondence to Serkan Eryılmaz.

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Eryılmaz, S., Stepanov, A. Runs in an ordered sequence of random variables. Metrika 67, 299–313 (2008). https://doi.org/10.1007/s00184-007-0134-7

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  • DOI: https://doi.org/10.1007/s00184-007-0134-7

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