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- W4366991683 abstract "Abstract We study the coupon collector’s problem with group drawings. 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 $ntoinfty$ , of the number $Z_{n,s}(k_n)$ of coupons that have not been drawn in the first $k_n$ drawings. Using a size-biased coupling construction together with Stein’s method for normal approximation, a quantitative central limit theorem for $Z_{n,s}(k_n)$ is shown for the case that $k_n=({n/s})(alphalog(n)+x)$ , where $0<alpha<1$ and $xinmathbb{R}$ . The same coupling construction is used to retrieve a quantitative Poisson limit theorem in the boundary case $alpha=1$ , again using Stein’s method." @default.
- W4366991683 created "2023-04-27" @default.
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- W4366991683 date "2023-04-25" @default.
- W4366991683 modified "2023-10-17" @default.
- W4366991683 title "Approaching the coupon collector’s problem with group drawings via Stein’s method" @default.
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- W4366991683 doi "https://doi.org/10.1017/jpr.2023.6" @default.
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