2022/02/15 by Carina Betken, Betken, Carina, Christoph Thäle +1
Mathematics · #60C05 #60F05 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2202.07485
openalex publication_date 2022/02/15 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper the coupon collector's problem with group drawings is studied. Assume there are n different coupons. At each time precisely s of the n coupons are drawn, where all choices are supposed to have equal probability. The focus lies on the fluctuations, as n→∞, of the number Zn,s(kn) of coupons that have not been drawn in the first kn drawings. Using a size-biased coupling construction together with Stein's method for normal approximation, a quantitative central limit theorem for Zn,s(kn) is shown for the case that kn=n\over s(αlog(n)+x), where 0