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  • 1 University of Szeged Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute Aradi vértanúk tere 1 H-6720 Szeged Hungary
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A collector samples with replacement a set of n ≧ 2 distinct coupons until he has nm , 0 ≦ m < n , distinct coupons for the first time. We refine the limit theorems concerning the standardized random number of necessary draws if n → ∞ and m is fixed: we give a one-term asymptotic expansion of the distribution function in question, providing a better approximation of it, than the one given by the limiting distribution function, and proving in particular that the rate of convergence in these limiting theorems is of order (log n )/ n .

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