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The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample

Author

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  • Henze, Norbert
  • Klein, Timo

Abstract

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454-466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the reasoning given by Matthews and Rukhin are pointed out and corrected.

Suggested Citation

  • Henze, Norbert & Klein, Timo, 1996. "The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 228-239, May.
    • Handle: RePEc:eee:jmvana:v:57:y:1996:i:2:p:228-239
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    Cited by:

    1. Schulte, Matthias & Thäle, Christoph, 2012. "The scaling limit of Poisson-driven order statistics with applications in geometric probability," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4096-4120.
    2. Tang, Ping & Lu, Rongrong & Xie, Junshan, 2022. "Asymptotic distribution of the maximum interpoint distance for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 190(C).
    3. Lao, W. & Mayer, M., 2008. "U-max-statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2039-2052, October.
    4. M. J. Appel & R. P. Russo, 2006. "Limiting Distributions for the Maximum of a Symmetric Function on a Random Point Set," Journal of Theoretical Probability, Springer, vol. 19(2), pages 365-375, June.

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