Abstract
We consider a generalized form of the coupon collection problem in which a random number,S, of balls is drawn at each stage from an urn initially containingnwhite balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after thekndraws? Our analysis is asymptotic asn→ ∞. We concentrate on the case whenkndraws are made, wherekn/n→ ∞ (the superlinear case), although we sketch known results for other ranges ofkn. A Gaussian limit is obtained via a martingale representation for the lower superlinear range, and a Poisson limit is derived for the upper boundary of this range via the Chen-Stein approximation.
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