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Short distances, flat triangles and Poisson limits

Published online by Cambridge University Press:  14 July 2016

Bernard Silverman and
Tim Brown
Bernard Silverman*
Affiliation:
University of Oxford
Tim Brown*
Affiliation:
University of Cambridge
*
∗ Now at the University of Bath.
∗ Now at the University of Bath.
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Abstract

Motivated by problems in the analysis of spatial data, we prove some general Poisson limit theorems for the U-statistics of Hoeffding (1948). The theorems are applied to tests of clustering or collinearities in plane data; nearest neighbour distances are also considered.

Keywords

POISSON PROCESSWEAK CONVERGENCEDISSOCIATED RANDOM VARIABLEU-STATISTICCLUSTERINGCOLLINEARITIESARCHAEOLOGYNEAREST NEIGHBOURPOINT PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978, pp. 815 - 825
Copyright
Copyright © Applied Probability Trust 1978 

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