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Asymptotics of the rising moments for the coupon collector's problem

   
@article{EJP1746,
	author = {Aristides Doumas and Vassilis Papanicolaou},
	title = {Asymptotics of the rising moments for the coupon collector's problem},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {18},
	year = {2013},
	keywords = {Coupon collector's problem, higher asymptotics},
	abstract = {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.},
	pages = {no. 41, 1-15},
	issn = {1083-6489},
	doi = {10.1214/EJP.v18-1746},    
        url = {http://ejp.ejpecp.org/article/view/1746}}