06 June 2014 3 2K Report

Negative binomial random variable with parameter r and p can be thought of as the number of attempts before rth success. This is a generalised form of geometric random variable with n=1. I am interested in calculating the expectation of max of N negative binomial random variables which are independent and identically distributed (i.i.d.). The difficulty that I am facing is that there is no known closed form formula for cumulative distribution function (CDF) of negative binomial random variables, therefore I can not apply the multiplication rule to the CDF of max of N negative binomial random variables.

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