Abstract. A collector samples with replacement a set of $n\ge2$ distinct coupons until he has, for the first time, all the coupons with only $m_n\in\{0,1,\ldots,n-1\} $ missing. If $m_n\to\infty $ and $(n-m_n)/\sqrt{n}\to\infty $ as $n\to\infty $, then the asymptotic distribution of the standardized random number of necessary draws is normal. With a Fourier-analytic method, we give a bound for the rates of convergence in these central limit theorems.

AMS Subject Classification (1991): 60F05

Received November 10, 2006. (Registered under 5969/2009.)