## 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.

### MSC:

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

### Keywords:

coupon collector’s problem; higher asymptotics
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