Runs in an ordered sequence of random variables

Abstract

Let X(1),..., X(n) be independent and identically distributed random variables with continuous distribution function. Denote by X(1:n) <= ... <= X(n:n) the corresponding order statistics. In the present paper, the concept of epsilon-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) <= ... <= X(n:n).