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On an interval splitting problem

Author

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

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.

Suggested Citation

  • Bruss, F. Thomas & Jammalamadaka, S. Rao & Zhou, Xian, 1990. "On an interval splitting problem," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 321-324, September.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:4:p:321-324
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    Cited by:

    1. Itoh, Yoshiaki & Mahmoud, Hosam & Smythe, Robert, 2006. "Probabilistic analysis of maximal gap and total accumulated length in interval division," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1356-1363, July.

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