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We study in this paper a generalized coupon collector problem, which consists in determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an…

Probability · Mathematics 2014-02-24 Emmanuelle Anceaume , Yann Busnel , Bruno Sericola

The Coupon Collector Problem (CCP) is a well-known combinatorial problem that seeks to estimate the number of random draws required to complete a collection of $n$ distinct coupon types. Various generalizations of this problem have been…

Data Structures and Algorithms · Computer Science 2026-01-21 Hadas Abraham , Ido Feldman , Eitan Yaakobi

We address a conjecture of Schilling concerning the optimality of the uniform distribution in the generalized Coupon Collector's Problem (CCP) where, in each round, a subset (package) of $s$ coupons is drawn from a total of $n$ distinct…

Probability · Mathematics 2026-05-12 Daniel Berend , Tomer Sher

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…

Probability · Mathematics 2026-05-11 Daniel Berend , Tomer Sher

This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets $d$ distinct coupons each run and she chooses the one that she has the least so far. On the asymptotic case when the number…

Information Theory · Computer Science 2019-07-10 Weiyu Xu , Ao Kevin Tang

In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-14 Dan Alistarh , Peter Davies

We examine the negative occupancy distribution and the coupon-collector distribution, both of which arise as distributions relating to hitting times in the extended occupancy problem. These distributions constitute a full solution to a…

Probability · Mathematics 2022-01-11 Ben O'Neill

In this note we evaluate the expected waiting time to complete a collection of coupons, in the case of coupons which arrives in groups of constant size, independently and with unequal probabilities. As an application we will be able to…

Probability · Mathematics 2012-10-08 Marco Ferrante , Nadia Frigo

We consider a generalisation of the classical coupon collector problem. We define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In each round, a random $r$-subset from the universe is drawn and all its $s$-subsets are…

Probability · Mathematics 2023-09-13 Siva Athreya , Satyaki Mukherjee , Soumendu Sundar Mukherjee

This Ph.D. thesis concerns the version of the classical coupon collector's problem, when a collector samples with replacement a set of $n\ge 2$ distinct coupons so that at each time any one of the $n$ coupons is drawn with the same…

Probability · Mathematics 2010-07-27 Anna Pósfai

We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…

Probability · Mathematics 2026-05-15 Luke J. Attrill , Timothy M. Garoni

This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of…

Discrete Mathematics · Computer Science 2017-03-07 Christian Berthet

We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting…

Discrete Mathematics · Computer Science 2025-07-22 Andrew Tan , Oriel Limor , Daniella Bar-Lev , Ryan Gabrys , Zohar Yakhini , Paul H. Siegel

We consider an extended variant of the classical coupon collector's problem with infinite number of collections. An arriving coupon is placed in the $r^{th}$ collection, $r\ge0$, if $r$ is the smallest index such that the corresponding…

Probability · Mathematics 2020-02-04 Andrii Ilienko

Motivated by a problem in the theory of randomized search heuristics, we give a very precise analysis for the coupon collector problem where the collector starts with a random set of coupons (chosen uniformly from all sets). We show that…

Discrete Mathematics · Computer Science 2017-08-01 Benjamin Doerr , Carola Doerr

In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…

Combinatorics · Mathematics 2023-02-22 Tipaluck Krityakierne , Thotsaporn Aek Thanatipanonda

In this paper the coupon collector's problem with group drawings is studied. Assume there are $ n $ different coupons. At each time precisely $ s $ of the $ n $ coupons are drawn, where all choices are supposed to have equal probability.…

Probability · Mathematics 2022-02-16 Carina Betken , Christoph Thäle

This paper is about the Coupon collector's problem. There are some coupons, or baseball cards, or other plastic knick-knacks that are put into bags of chips or under soda bottles, etc. A collector starts collecting these trinkets and wants…

Probability · Mathematics 2020-03-11 Rohit Pandey

In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.

Probability · Mathematics 2016-09-15 Marco Ferrante , Alessia Tagliavini

A collector wishes to collect $m$ complete sets of $N$ distinct coupons. The draws from the population are considered to be independent and identical distributed with replacement, and the probability that a type-$j$ coupon is drawn is noted…

Probability · Mathematics 2015-11-02 Aristides V. Doumas , Vassilis G. Papanicolaou
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