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Maximum Statistics of N Random Variables Distributed by the Negative Binomial Distribution

Published online by Cambridge University Press:  01 June 1997

PETER J. GRABNER  and
HELMUT PRODINGER
PETER J. GRABNER
Affiliation:
Institut für Mathematik A, Steyrergasse 30, A–8010 Graz, Austria (e-mail: grabner@weyl.math.tu_graz.ac.at)
HELMUT PRODINGER
Affiliation:
Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstrasse 8–10, A–1040 Wien, Austria (e-mail: Helmut.Prodinger@tuwien.ac.at)
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Abstract

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The lifetime of a player is defined to be the time where he gets his b-th hit, where a hit will occur with probability p. We consider the maximum statistics of N independent players. For b≠1 this is significantly more difficult than the known instance b=1. The expected value of the maximum lifetime of N players is given by logQN+(b−1)logQ logQN+ smaller order terms, where Q=1/(1−p).

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 2 , June 1997 , pp. 179 - 183
Copyright
1997 Cambridge University Press