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Limit theorems for the diameter of a random sample in the unit ball

Mayer, Michael ; Molchanov, Ilya

In: Extremes, 2007, vol. 10, no. 3, p. 129-150

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    Titre
    • Limit theorems for the diameter of a random sample in the unit ball
    Auteur
    • Mayer, Michael. Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
    • Molchanov, Ilya. Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Extremes, 2007, vol. 10, no. 3, p. 129-150. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:311708
    Summary
    We prove a limit theorem for the maximum interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit d-dimensional ball for d≥2. The results are specialised for the cases when the points have spherical symmetric distributions, in particular, are uniformly distributed in the whole ball and on its boundary. Among other examples, we also give results for distributions supported by pointed sets, such as a rhombus or a family ofsegments