### Abstract

Let X_{1}, X_{2},..., be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I_{1}(0) = [0, 1] and let I_{k}(n) denote the kth largest interval generated by the points 0, X_{1}, X_{2},..., X_{n-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 I_{k(n)}(n) be hit (a.s.) only finitely often, as well as infinitely often.

Original language | English |
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Pages (from-to) | 321-324 |

Number of pages | 4 |

Journal | Statistics and Probability Letters |

Volume | 10 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

### Keywords

- extended Borel-Cantelli lemma
- Interval splitting
- spacing

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## Cite this

Bruss, F. T., Jammalamadaka, S. R., & Zhou, X. (1990). On an interval splitting problem.

*Statistics and Probability Letters*,*10*(4), 321-324. https://doi.org/10.1016/0167-7152(90)90049-D