For a spherically symmetric multivariate normal random sample, the asymptotic distribution of the largest interpoint Euclidean distance is derived. The number of interpoint distances exceeding a high level is shown to have a limiting Poisson distribution.
Publié le : 1993-05-14
Classification:
Normal sample range,
$U$-statistic,
Poisson clumping heuristic,
exceedance,
60E05,
60F99,
62E20,
62H10
@article{1177005433,
author = {Matthews, Peter C. and Rukhin, Andrew L.},
title = {Asymptotic Distribution of the Normal Sample Range},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 454-466},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005433}
}
Matthews, Peter C.; Rukhin, Andrew L. Asymptotic Distribution of the Normal Sample Range. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 454-466. http://gdmltest.u-ga.fr/item/1177005433/