arXiv Open Access 2025

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

Costacèque Decreusefond

Lihat Sumber

Abstrak

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 \textit{e.g.} Gaussian, Pareto, \textit{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.

Topik & Kata Kunci

math.PR

Penulis (2)

Costacèque

Decreusefond

Format Sitasi

APA MLA BibTeX

Costacèque, Decreusefond (2025). Convergence rate for the coupon collector's problem with Stein's method. https://arxiv.org/abs/2501.06535

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓