Coupon collector's problem and generalized Pareto distributions

Let Nn={1,2,…,n}Nn={1,2,…,n}. We sample with replacement from the set NnNn 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 collector's problem. We investigate models for the asymptotic behavior of the excesses of Mn over the high thresholds.