A collector samples with replacement a set of
≧ 2 distinct coupons until he has
, 0 ≦
, distinct coupons for the first time. We refine the limit theorems concerning the standardized random number of necessary draws if
→ ∞ and
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
Baum, L. E. and Billingsley, P.
, Asymptotic distributions for the coupon collector’s problem,
Ann. Math. Statist.
Billingsley P., 'Asymptotic distributions for the coupon collector’s problem' (1965) 36Ann. Math. Statist.: 1835-1839.
Billingsley P.Asymptotic distributions for the coupon collector’s problemAnn. Math. Statist.19653618351839)| false