Coupon collectorʹs problem and generalized Pareto distributions

Let N n = { 1 , 2 , … , n } . We sample with replacement from the set N n assuming that each element has probability 1/n of being drawn. Let Mn be the waiting time determined by certain stoping rules in the coupon collectorʹs problem. We investigate models for the asymptotic behavior of the excesses of Mn over the high thresholds.