## 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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