PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 71(85), pp. 41--53 (2002)
TAUBERIAN THEOREMS AND LIMIT DISTRIBUTIONS FOR UPPER ORDER STATISTICS
H. Lanzinger and U. StadtmüllerUniversität Ulm, Abt. f. Zahlen- u. Wahrscheinlichkeitstheorie, 89069 Ulm, Germany
Abstract: Starting with the Tauberian theorems of Karamata for regular variation we prove a slight extension of a Tauberian theorem by Trautner and the second author and use this to characterize limit relations for upper order statistics if we are in the domain of attraction of a max-stable distribution. Furthermore, we discuss the speed of convergence therein.
Keywords: integral transforms; regular variation
Classification (MSC2000): 44A05; 60F99;60G70
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