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October, 1975 A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities
Raymond J. Huntington, Joseph I. Naus
Ann. Probab. 3(5): 894-896 (October, 1975). DOI: 10.1214/aop/1176996278

Abstract

Given $N$ points distributed at random on $\lbrack 0, 1)$, let $p_n$ be the size of the smallest interval that contains $n$ points. Previous work finds $\operatorname{Pr}(p_n \leqq p)$ for all $n, N$, and rational $p$. The present note derives a new and considerably simplified formula for $\operatorname{Pr}(p_n \leqq p)$ for all $n, N$, and $p$.

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Raymond J. Huntington. Joseph I. Naus. "A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities." Ann. Probab. 3 (5) 894 - 896, October, 1975. https://doi.org/10.1214/aop/1176996278

Information

Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0316.60014
MathSciNet: MR388492
Digital Object Identifier: 10.1214/aop/1176996278

Subjects:
Primary: 60E05

Keywords: Clusters , Coincidences , interarrival times , maximum clusters , Nearest neighbor distances , smallest intervals

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • October, 1975
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