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On an interval splitting problem

par Bruss, F Thomas ;Rao Jammalamadaka, Sreenivasa;Zhou, Xian
Référence Statistics & probability letters, 10, 4, page (321-324)
Publication Publié, 1990

Article révisé par les pairs

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Résumé :

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.