Asymptotics of the rising moments for the coupon collector%26apos;s problem

作者：Doumas Aristides V^*; Papanicolaou Vassilis G

来源：Electronic Journal of Probability, 2013, 18(0): 1-15.

DOI：10.1214/EJP.v18-1746

• Coupon collector%26apos
• s problem
• higher asymptotics

We develop techniques of computing the asymptotics of the so-called rising 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 -%26gt; infinity. 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 families of coupon probabilities, after adopting a dichotomy, we arrive at the leading behavior of the rising moments of T-N as N -%26gt; infinity. We also present various illustrative examples.

• 出版日期2013-3-22