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


 
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1. Title Title of document Asymptotics of the rising moments for the coupon collector's problem
 
2. Creator Author's name, affiliation, country Aristides V Doumas; National Technical University of Athens; Greece
 
2. Creator Author's name, affiliation, country Vassilis G Papanicolaou; National Technical University of Athens; Greece
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Coupon collector's problem, higher asymptotics
 
3. Subject Subject classification 60F05, 60F99
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2013-03-22
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1746
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-1746
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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