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The limit distribution of the largest nearest-neighbour link in the unit d-cube

Published online by Cambridge University Press:  14 July 2016

Holger Dette  and
Norbert Henze
Holger Dette*
Affiliation:
University of Hannover
Norbert Henze*
Affiliation:
University of Hannover
*
∗Postal address: Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000 Hannover 1, W. Germany.
∗Postal address: Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000 Hannover 1, W. Germany.
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Abstract

Let·p denote the p-norm on . For n points drawn independently and uniformly from the unit d-cube, we obtain the limit distribution of the largest nearest-neighbour link (with respect to | · |p) in the cases ; (2) d = 3, p = 1, 2, ∞and (3) 4, p =∞.

Keywords

COMPUTATIONAL GEOMETRYNEAREST-NEIGHBOUR DISTANCESEXTREME-VALUE DISTRIBUTIONBOUNDARY DOMINATIONLIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 67 - 80
Copyright
Copyright © Applied Probability Trust 1989 

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References

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Steele, J. M. and Tierney, L. (1986) Boundary domination and the distribution of the largest nearest neighbour link. J. Appl. Prob. 23, 524–528.Google Scholar