On an interval splitting problem

F. Thomas Bruss, S. Rao Jammalamadaka and Xian Zhou

Statistics & Probability Letters, 1990, vol. 10, issue 4, 321-324

Abstract: Let X1, X2,..., be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I1(0) = [0, 1] and let Ik(n) denote the kth largest interval generated by the points 0, X1, X2,..., Xn-1, 1 (or equivalently, the interval corresponding to the kth largest spacing at the nth stage). This note studies the question for which classes of sequences k = k(n), will the interval Ik(n)(n) be hit (a.s.) only finitely often, as well as infinitely often.

Keywords: Interval; splitting; spacing; extended; Borel--Cantelli; lemma (search for similar items in EconPapers)
Date: 1990
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