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Asymptotic Distribution Of The Maximum Interpoint Distance In A Sample Of Random Vectors With A Spherically Symmetric Distribution
Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93106 USA..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 25, no 6, 3571-3591 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 25, no 6, 3571-3591 p.
Keyword [en]
Maximum interpoint distance, extreme value distributions, Gumbel distribution
National Category
URN: urn:nbn:se:uu:diva-267176DOI: 10.1214/14-AAP1082ISI: 000363223100015OAI: oai:DiVA.org:uu-267176DiVA: diva2:872767
Knut and Alice Wallenberg Foundation
Available from: 2015-11-20 Created: 2015-11-19 Last updated: 2016-02-17Bibliographically approved

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