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The limit distribution of the largest interpoint distance for distributions supported by a d-dimensional ellipsoid and generalizations

  • Michael Schrempp (a1)

We study the asymptotic behaviour of the maximum interpoint distance of random points in a d-dimensional ellipsoid with a unique major axis. Instead of investigating only a fixed number of n points as n tends to ∞, we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. Our main result covers the case of uniformly distributed points.

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* Postal address: Institute of Stochastics, Karlsruhe Institute of Technology, Englerstr. 2, D-76131 Karlsruhe, Germany. Email address:
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[1] M. J. B. Appel , C. A. Najim and R. P. Russo (2002). Limit laws for the diameter of a random point set. Adv. Appl. Prob. 34, 110.

[2] P. Billingsley (1999). Convergence of Probability Measures, 2nd edn. John Wiley, New York>.

[3] D. J. Daley and D. Vere-Jones (2008). An Introduction to the Theory of Point Processes, Vol. II, General Theory and Structure, 2nd edn. Springer, New York.

[4] Y. Demichel , A.-K. Fermin and P. Soulier (2015). The diameter of a random elliptical cloud. Electron. J. Prob. 20, 27, 32pp.

[5] N. Henze and T. Klein (1996). The limit distribution of the largest interpoint distance from a symmetric Kotz sample. J. Multivariate Analysis 57, 228239.

[7] S. R. Jammalamadaka and S. Janson (2015). Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution. Ann. Appl. Prob. 25, 35713591.

[10] P. C. Matthews and A. L. Rukhin (1993). Asymptotic distribution of the normal sample range. Ann. Appl. Prob. 3, 454466.

[11] M. Mayer and I. Molchanov (2007). Limit theorems for the diameter of a random sample in the unit ball. Extremes 10, 129150.

[12] S. I. Resnick (1987). Extreme Values, Regular Variation, and Point Processes, Springer, New York.

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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