Asymptotic Results for Uniform Group Drawing in the Coupon Collector's Problem

Daniel Berend; Tomer Sher

Asymptotic Results for Uniform Group Drawing in the Coupon Collector's Problem

Probability 2026-05-11 v1

Authors: Daniel Berend , Tomer Sher

Abstract

The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons selected uniformly at random from a set of $n$ coupons. We focus on three regimes of the package size $s$ : (i) constant $s$ , (ii) $s$ proportional to $n$ , and (iii) $s$ "very close" to $n$ . For each case, we provide precise asymptotic expressions for the expected collection time. Keywords: Coupon Collector's Problem, Group Drawings, Uniform Distribution, Asymptotic Analysis, Expected Collection Time

Keywords

Coupon Collector's Problem Group Drawings Uniform Distribution Asymptotic Analysis Expected Collection Time

Cite

@article{arxiv.2605.06953,
  title  = {Asymptotic Results for Uniform Group Drawing in the Coupon Collector's Problem},
  author = {Daniel Berend and Tomer Sher},
  journal= {arXiv preprint arXiv:2605.06953},
  year   = {2026}
}

Comments

This article and arXiv:2509.17201 together supersede the original preprint, following their acceptance as two separate papers in Stochastic Models. This part focuses on asymptotic results for uniform group drawing in the coupon collector's problem

Asymptotic Results for Uniform Group Drawing in the Coupon Collector's Problem

Abstract

Keywords

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