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Tail expansions for random record distributions

Published online by Cambridge University Press:  26 March 2001

RUDOLF GRÜBEL  and
NIKLAS VON ÖHSEN
RUDOLF GRÜBEL
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany; e-mail: rgrubel@stochastik.uni hannover.de
NIKLAS VON ÖHSEN
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany; e-mail: rgrubel@stochastik.uni hannover.de
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Abstract

The random record distribution ν associated with a probability distribution μ can be written as a convolution series, ν = [sum ]∞n=1n−1 (n + 1)−1μ*n. Various authors have obtained results on the behaviour of the tails ν((x, ∞)) as x → ∞, using Laplace transforms and the associated Abelian and Tauberian theorems. Here we use Gelfand transforms and the Wiener–Lévy–Gelfand Theorem to obtain expansions of the tails under moment conditions on μ. The results differ notably from those known for other convolution series.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 2 , March 2001 , pp. 365 - 382
Copyright
2001 Cambridge Philosophical Society

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