Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T06:18:36.686Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

Abstract

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).

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)