Coupon collector's probabilities and generating function: analytic approach

2016/09/05 by Andrea Monsellato, Monsellato, Andrea
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Database Systems and Queries #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #Probability (math.PR) #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1609.01066

arxiv created 2016/09/05 · openalex publication_date 2016/09/05 · arxiv updated 2016/09/06 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \citePolyaUrn, starting from a particular type of recurrence differential equation it is used an analytic approach to recover explicit probabilities and generating function. Note that this kind of recurrence differential equations often appear in Polya Urn context \citePolyaUrn.

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• Convergence of Coupon Collecting Process via Wormald's Differential Equation Method
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• Approximation Theorems Related to the Coupon Collector's Problem