Convergence rate for the coupon collector’s problem with Stein’s method

Bruno Costacèque and Laurent Decreusefond

Stochastic Processes and their Applications, 2026, vol. 193, issue C

Abstract: The functional characterization of a measure, an essential but delicate aspect of Stein’s method, is shown to be accessible for stable probability distributions on convex cones. This notion encompasses the usual stable distributions e.g. Gaussian, Pareto, etc. but also the max-stable distributions: Weibull, Gumbel and Fréchet. We use the definition of max-stability to define a Markov process whose invariant measure is the stable measure of interest. In this paper, we focus on the Gumbel distribution and show how this construction can be applied to estimate the rate of convergence in the classical coupon collector’s problem.

Keywords: Coupon collector’s problem; Gumbel distribution; Stein’s method; Generator approach (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104835

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