Convergence rate for the coupon collector's problem with Stein's method
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917375505334272 |
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| author | Costacèque Decreusefond |
| author_facet | Costacèque Decreusefond |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence rate for the coupon collector's problem with Stein's method Costacèque Decreusefond Probability 60F07 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. |
| title | Convergence rate for the coupon collector's problem with Stein's method |
| topic | Probability 60F07 |
| url | https://arxiv.org/abs/2501.06535 |