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Consider a vector of $n$ integer variables with initial values of 0. Each step we take random $w_i\thicksim NB(q, l)$ (independent randon values with the same negative binomial distribution) and add it to the variable with the minimal current value, even cases go to the leftmost of the equal variables. What is the CDF of the maximal value in the vector at a given step?

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  • $\begingroup$ This is what stochastic simulation is for. $\endgroup$
    – Mark L. Stone
    Commented Mar 21, 2020 at 14:36
  • $\begingroup$ But it looks like a common optimization case, may there be an analytic expression? $\endgroup$
    – Ihnatus
    Commented Mar 22, 2020 at 9:23

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