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On the total time spent in records by a discrete uniform sequence

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rudolf Grübel  and
Anke Reimers
Rudolf Grübel*
Affiliation:
Universität Hannover
Anke Reimers*
Affiliation:
Universität Hannover
*
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
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Abstract

We consider the sum S d of record values in a sequence of independentrandom variables that are uniformly distributed on 1,…,d. This sum can be interpreted as the total amount of time spent in record lifetimes in the standard renewal theoretic setup. We investigate the distributional limit of S d and some related quantities as d→∞. Some explicit values are given for d=6, a case that can be interpreted as a simple game of chance.

Keywords

Recordsuniform distributionperpetuities

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60K05: Renewal theory

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 768 - 775
Copyright
Copyright © by the Applied Probability Trust 2001 

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