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December 2015 Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution
Sreenivasa Rao Jammalamadaka, Svante Janson
Ann. Appl. Probab. 25(6): 3571-3591 (December 2015). DOI: 10.1214/14-AAP1082

Abstract

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum “interpoint distance,” in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complements our earlier study on the minimum interpoint distance.

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Sreenivasa Rao Jammalamadaka. Svante Janson. "Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution." Ann. Appl. Probab. 25 (6) 3571 - 3591, December 2015. https://doi.org/10.1214/14-AAP1082

Information

Received: 1 December 2012; Revised: 1 November 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1328.60027
MathSciNet: MR3404644
Digital Object Identifier: 10.1214/14-AAP1082

Subjects:
Primary: 60D05, 60F05, 60G70, 62E20

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 6 • December 2015
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