On an interval splitting problem

F. Thomas Bruss; S. Rao Jammalamadaka; Xian Zhou

doi:10.1016/0167-7152(90)90049-D

On an interval splitting problem

F. Thomas Bruss^*, S. Rao Jammalamadaka, Xian Zhou

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 I_k(n) denote the kth largest interval generated by the points 0, X₁, X₂,..., 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
Pages (from-to)	321-324
Number of pages	4
Journal	Statistics and Probability Letters
Volume	10
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(90)90049-D
Publication status	Published - 1990
Externally published	Yes

Keywords

extended Borel-Cantelli lemma
Interval splitting
spacing

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10.1016/0167-7152(90)90049-D

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title = "On an interval splitting problem",

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 = "extended Borel-Cantelli lemma, Interval splitting, spacing",

author = "Bruss, {F. Thomas} and Jammalamadaka, {S. Rao} and Xian Zhou",

year = "1990",

doi = "10.1016/0167-7152(90)90049-D",

language = "English",

volume = "10",

pages = "321--324",

journal = "Statistics and Probability Letters",

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T1 - On an interval splitting problem

AU - Bruss, F. Thomas

AU - Jammalamadaka, S. Rao

AU - Zhou, Xian

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

KW - extended Borel-Cantelli lemma

KW - Interval splitting

KW - spacing

UR - http://www.scopus.com/inward/record.url?scp=38249017579&partnerID=8YFLogxK

U2 - 10.1016/0167-7152(90)90049-D

DO - 10.1016/0167-7152(90)90049-D

M3 - Article

AN - SCOPUS:38249017579

VL - 10

SP - 321

EP - 324

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -

On an interval splitting problem

Abstract

Keywords

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