The Annals of Applied Probability

Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution

Sreenivasa Rao Jammalamadaka and Svante Janson

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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.

Article information

Ann. Appl. Probab., Volume 25, Number 6 (2015), 3571-3591.

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

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Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F05: Central limit and other weak theorems 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory

Maximum interpoint distance extreme value distributions Gumbel distribution


Jammalamadaka, Sreenivasa Rao; Janson, Svante. Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution. Ann. Appl. Probab. 25 (2015), no. 6, 3571--3591. doi:10.1214/14-AAP1082.

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