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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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