Asymptotics of the rising moments for the coupon collector’s problem. (English) Zbl 1283.60035

Summary: We develop techniques of computing the asymptotics of the moments of the number \(T_N\) of coupons that a collector has to buy in order to find all \(N\) existing different coupons as \(N\rightarrow \infty\). The probabilities (occurring frequencies) of the coupons can be quite arbitrary. After mentioning the case where the coupon probabilities are equal, we consider the general case (of unequal probabilities). For a large class of distributions (after adopting a dichotomy) we arrive at the leading behavior of the moments of \(T_N\) as \(N\rightarrow \infty\). We also present various illustrative examples.


60F05 Central limit and other weak theorems
60F99 Limit theorems in probability theory
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