Results and conjectures on the role of the uniform distribution in the coupon collector's problem with group drawings

2021 ◽  
Vol 169 ◽  
pp. 106112
Author(s):  
Judith Schilling
Keyword(s):  
Uniform Distribution ◽  
Coupon Collector’S Problem ◽  
Coupon Collector's Problem

On the transition probabilities of the move-to-front scheme

1994 ◽  
Vol 31 (02) ◽  
pp. 570-574 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Transition Probabilities ◽  
Coupon Collector’S Problem ◽  
Coupon Collector's Problem

The transition probabilities of the move-to-front scheme are obtained by exploiting the connection between it and the coupon-collector's problem.

scholarly journals A cutoff time strategy based on the coupon collector’s problem

2020 ◽  
Vol 286 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Fernando G. Lobo ◽  
Mosab Bazargani ◽  
Edmund K. Burke
Keyword(s):  
Coupon Collector’S Problem ◽  
Coupon Collector's Problem

scholarly journals The Coupon Collector's Problem Revisited: Asymptotics of the Variance

2012 ◽  
Vol 44 (1) ◽  
pp. 166-195 ◽  
Author(s):  
Aristides V. Doumas ◽  
Vassilis G. Papanicolaou
Keyword(s):  
Large Class ◽  
Limit Distribution ◽  
Limit Theorems ◽  
Gumbel Distribution ◽  
Coupon Collector’S Problem ◽  
Second Moments ◽  
General Limit ◽  
Coupon Collector's Problem

We develop techniques for computing the asymptotics of the first and second moments of the number TN of coupons that a collector has to buy in order to find all N existing different coupons as N → ∞. The probabilities (occurring frequencies) of the coupons can be quite arbitrary. From these asymptotics we obtain the leading behavior of the variance V[TN] of TN (see Theorems 3.1 and 4.4). Then, we combine our results with the general limit theorems of Neal in order to derive the limit distribution of TN (appropriately normalized), which, for a large class of probabilities, turns out to be the standard Gumbel distribution. We also give various illustrative examples.

Limit Theorems for an Extended Coupon Collector's Problem and for Successive Subsampling with Varying Probabilites*

1980 ◽  
Vol 29 (3-4) ◽  
pp. 113-132 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Asymptotic Normality ◽  
Limit Theorems ◽  
Finite Population ◽  
Waiting Times ◽  
Invariance Principles ◽  
Weak Invariance ◽  
Coupon Collector’S Problem ◽  
Asymptotic Distribution Theory ◽  
Multistage Sampling ◽  
Coupon Collector's Problem

Asymptotic normality as well as some weak invariance principles for bonus sums and waiting times in an extended coupon collector's problem are considered and incorporated in the study of the asymptotic distribution theory of estimators of (finite) population totals in successive sub-sampling (or multistage sampling) with varying probabilities (without replacement). Some applications of these theorems are also considered.

scholarly journals Poisson Approximation in a Poisson Limit Theorem Inspired by Coupon Collecting

2009 ◽  
Vol 46 (02) ◽  
pp. 585-592
Author(s):  
Anna Pósfai
Keyword(s):  
Limit Theorem ◽  
Waiting Time ◽  
Random Variables ◽  
Poisson Approximation ◽  
Poisson Law ◽  
Coupon Collector’S Problem ◽  
Poisson Limit ◽  
Coupon Collector's Problem ◽  
Error Order

In this paper we refine a Poisson limit theorem of Gnedenko and Kolmogorov (1954): we determine the error order of a Poisson approximation for sums of asymptotically negligible integer-valued random variables that converge in distribution to the Poisson law. As an application of our results, we investigate the case of the coupon collector's problem when the distribution of the collector's waiting time is asymptotically Poisson.

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