Limit distributions of norms of vectors of positive i.i.d. random variables


Schlather, Martin


Document Type: Article
Year of publication: 2001
The title of a journal, publication series: Annals of Probability
Volume: 29
Issue number: 2
Page range: 862-881
Place of publication: New York, NY [u.a.]
Publishing house: Inst. of Mathematical Statistics
ISSN: 0091-1798
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematische Statistik (Schlather 2012-)
Subject: 510 Mathematics
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.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.




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Schlather, Martin (2001) Limit distributions of norms of vectors of positive i.i.d. random variables. Annals of Probability New York, NY [u.a.] 29 2 862-881 [Article]


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