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

DOI10.1214/14-AAP1082zbMath1328.60027arXiv1211.0822OpenAlexW1882048592MaRDI QIDQ894816

Svante Janson, Sreenivasa Rao Jammalamadaka

Publication date: 24 November 2015

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0822

zbMATH Keywords

extreme value distributionsGumbel distributionmaximum interpoint distance

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70)

Related Items (4)

Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set ⋮ Extremal random beta polytopes ⋮ Large nearest neighbour balls in hyperbolic stochastic geometry ⋮ Asymptotic distribution of the maximum interpoint distance for high-dimensional data

Cites Work

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• Asymptotic distribution of the normal sample range
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• \(U\)-max-statistics
• Limit theorems for diameter of a random sample in the unit ball
• Extremes and related properties of random sequences and processes
• Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
• The limit distribution of the largest interpoint distance from a symmetric Kotz sample
• Short distances, flat triangles and Poisson limits
• Limit laws for the diameter of a random point set
• Cycles and Unicyclic Components in Random Graphs

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