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December, 1979 Asymptotic Normality of Sum-Functions of Spacings
Lars Holst
Ann. Probab. 7(6): 1066-1072 (December, 1979). DOI: 10.1214/aop/1176994901

Abstract

Take $n$ points at random on a circle of unit circumference and order them clockwise. Let $S^{(m)}_0,\cdots, S^{(m)}_{n-1}$ be the $m$th order spacings, i.e., the clockwise arc-lengths between every pair of points with $m - 1$ points between. Ordinary spacings correspond to the case $m = 1$. A central limit theorem is proved for $Z_n = \sum^{n-1}_{k=0}h(nS_k,\cdots, nS_{k+m-1})$, where $h$ is a given function. Using this, asymptotic distributions of central order statistics and sums of the logarithms of $m$th order spacings are derived.

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Lars Holst. "Asymptotic Normality of Sum-Functions of Spacings." Ann. Probab. 7 (6) 1066 - 1072, December, 1979. https://doi.org/10.1214/aop/1176994901

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0421.60017
MathSciNet: MR548902
Digital Object Identifier: 10.1214/aop/1176994901

Subjects:
Primary: 60F05
Secondary: 62E20

Keywords: limit theorems , order statistics , spacings , uniform distribution

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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