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April 2001 Limit Distributions Of Norms Of Vectors Of Positive I.I.D. Random Variables
Martin Schlather
Ann. Probab. 29(2): 862-881 (April 2001). DOI: 10.1214/aop/1008956695


This paper aims to combine the central limit theorem with the limit theorems in extreme value theory through a parametrized class of limit theorems where the former ones appear as special cases. To this end the limit distributions of suitably centered and normalized $l_{cp(n)}$-norms of $n$-vectors of positive i.i.d. random variables are investigated. Here, $c$ is a positive constant and $p(n)$ is a sequence of positive numbers that is given intrinsically by the form of the upper tail behavior of the random variables. A family of limit distributions is obtained if $c$ runs over the positive real axis. The normal distribution and the extreme value distributions appear as the endpoints of these families, namely, for $c =0 +$ and $c = \infty$, respectively.


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Martin Schlather. "Limit Distributions Of Norms Of Vectors Of Positive I.I.D. Random Variables." Ann. Probab. 29 (2) 862 - 881, April 2001.


Published: April 2001
First available in Project Euclid: 21 December 2001

zbMATH: 1014.60015
MathSciNet: MR1849180
Digital Object Identifier: 10.1214/aop/1008956695

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 2 • April 2001
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