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Related papers: On a generalisation of the coupon collector proble…

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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

We initiate the study of the Careless Coupon Collector's Problem (CCCP), a novel variation of the classical coupon collector, that we envision as a model for information systems such as web crawlers, dynamic caches, and fault-resilient…

Discrete Mathematics · Computer Science 2026-02-25 Emilio Cruciani , Aditi Dudeja

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

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

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

A collector samples coupons with replacement from a pool containing $g$ \textit{uniform} groups of coupons, where "uniform group" means that all coupons in the group are equally likely to occur. For each $j = 1, \dots, g$ let $T_j$ be the…

Probability · Mathematics 2018-11-13 Aristides V. Doumas , Vassilis G. Papanicolaou

To reduce computational complexity and delay in randomized network coded content distribution (and for some other practical reasons), coding is not performed simultaneously over all content blocks but over much smaller subsets known as…

Information Theory · Computer Science 2010-06-04 Yao Li , Emina Soljanin , Predrag Spasojevic

The solution of the classical Coupon Collector's Problem is based on the assumptions that all stickers are independently and uniformly distributed. We can prove statistically as well as analytically that in particular the assumption of…

Probability · Mathematics 2016-03-10 Niklas Braband , Sonja Braband , Malte Braband

The classic Coupon-Collector Problem (CCP) is generalized to the extent that each coupons serves certain "purposes". Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all $k$-element…

Probability · Mathematics 2014-01-20 Marcel Wild , Svante Janson , Stephan Wagner , Dirk Laurie

We study coverage processes in which each draw reveals a subset of $[n]$, and the goal is to determine the expected number of draws until all items are seen at least once. A classical example is the Coupon Collector's Problem, where each…

Information Theory · Computer Science 2025-10-30 Yitzchak Grunbaum , Eitan Yaakobi

The following variant of the collector's problem has attracted considerable attention relatively recently (see, e.g., N. Pintacuda 1980, D. Foata H. Guo-Niu and B. Lass 2001, D. Foata and D. Zeilberger 2003, I. Adler, S. Oren and S. Ross…

Probability · Mathematics 2014-12-16 Aristides V. Doumas , Vassilis G. Papanicolaou

We consider the following variant of the classic collector's problem: The family of coupon probabilities is the mixing of two subfamilies one of which is the \textit{uniform} family, while the other belongs to the well known \textit{Zipf…

Probability · Mathematics 2019-04-23 Aristides V. Doumas , Vassilis G. Papanicolaou

The "double Dixie cup problem" of D.J. Newman and L. Shepp (1960) is a well-known variant of the coupon collector's problem, where the object of study is the number $T_{m}(N)$ of coupons that a collector has to buy in order to complete $m$…

Probability · Mathematics 2015-11-06 Aristides V. Doumas , Vassilis G. Papanicolaou

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

To approximate the trajectories of a stochastic process by the solution of some differential equation is widely used in the fields of probability, computer science and combinatorics. In this paper, the convergence of coupon collecting…

Probability · Mathematics 2019-12-06 Anshui Li , Yong Chen

The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no…

History and Overview · Mathematics 2021-08-06 Niklas Braband , Sonja Braband , Malte Braband

A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to…

Probability · Mathematics 2020-05-13 Vassilis G. Papanicolaou , Aristides V. Doumas

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

We study a labeled variant of the classical Coupon Collector Problem (CCP), recently introduced by Tan et al., where coupons arrive in groups and only the set of labels is revealed. The goal is to determine the expected number of group…

Probability · Mathematics 2025-10-28 Dina Barak-Pelleg , Daniel Berend

Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the…

Discrete Mathematics · Computer Science 2017-06-19 Christian Berthet