On an interval splitting problem

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.

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Year of publication:	1990
Authors:	Bruss, F. Thomas ; Jammalamadaka, S. Rao ; Zhou, Xian
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 10.1990, 4, p. 321-324
Publisher:	Elsevier
Keywords:	Interval splitting spacing extended Borel-Cantelli lemma

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10005224049