The Annals of Probability

Limit Distributions Of Norms Of Vectors Of Positive i.i.d.Random Variables

Martin Schlather

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 29, Number 2 (2001), 862-881.

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956695

Digital Object Identifier
doi:10.1214/aop/1008956695

Mathematical Reviews number (MathSciNet)
MR1849180

Zentralblatt MATH identifier
1014.60015

Citation

Schlather, Martin. Limit Distributions Of Norms Of Vectors Of Positive i.i.d.Random Variables. Ann. Probab. 29 (2001), no. 2, 862--881. doi:10.1214/aop/1008956695. https://projecteuclid.org/euclid.aop/1008956695


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