Maximum Statistics of N Random Variables Distributed by the Negative Binomial Distribution
Peter J. Grabner, Helmut Prodinger · Combinatorics Probability Computing · 1997
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).