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On the weak limit law of the maximal uniform k-spacing

Part of: Nonparametric inference Stochastic processes Limit theorems

Published online by Cambridge University Press:  25 July 2016

Aleksandar Mijatović  and
Vladislav Vysotsky
Aleksandar Mijatović*
Affiliation:
King's College London
Vladislav Vysotsky*
Affiliation:
Arizona State University, Imperial College London, and St. Petersburg Department of Steklov Mathematical Institute
*
Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK. Email address: [email protected]
School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ 85287, USA. Email address: [email protected]
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Abstract

In this paper we give a simple proof of a limit theorem for the length of the largest interval straddling a fixed number of points that are independent and uniformly distributed on a unit interval. The key step in our argument is a classical theorem of Watson on the maxima of m-dependent stationary stochastic sequences.

Keywords

Maximal k-spacingorder statisticsuniform distribution

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G70: Extreme value theory; extremal processes 62G30: Order statistics; empirical distribution functions
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 235 - 238
Copyright
Copyright © Applied Probability Trust 2016 

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References

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