Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution
| Autor: | Jammalamadaka, Sreenivasa Rao, Janson, Svante |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Annals of Applied Probability 2015, Vol. 25, No. 6, 3571-3591 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/14-AAP1082 |
| Popis: | Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complements our earlier study on the minimum interpoint distance. Comment: Published at http://dx.doi.org/10.1214/14-AAP1082 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | arXiv |
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