A coupon collector samples with replacement distinct coupons (each with equal probability ). Let . The sampling is repeated until distinct coupons are collected for the first time. The waiting time, i.e., the random number of draws until coupons are obtained is denoted by . Let and denote mean and variance of and let denote the distribution function of the normalized random variable .
First limit theorems (for had been proved by P. Erdős and A. Rényi [Publ. Math. Inst. Hung. Acad. Sci., Ser. A 6, 215–220 (1961; Zbl 0102.35201)] (for ) and by L. E. Baum and P. Billingsley [Ann. Math. Stat. 36 1835–1839 (1965; Zbl 0227.62010)] (for ). In the second paper, it was also shown that is asymptotically normal.
In the paper under review, the author obtains rates of convergence for the asymptotic if and tend to .