Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-06T11:02:46.914Z Has data issue: false hasContentIssue false
  • English
  • Français

Dixie cups: sampling with replacement from a finite population

Part of: Limit theorems Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Chris A. J. Klaassen
Chris A. J. Klaassen*
Affiliation:
University of Amsterdam
*
∗Postal address: Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

At which (random) sample size will every population element have been drawn at least m times? This special coupon collector's problem is often referred to as the Dixie cup problem. Some asymptotic properties of the Dixie cup problem with unequal sampling probabilities are described.

Keywords

COUPON COLLECTOR'S PROBLEMEXTREME VALUESGAMMA DISTRIBUTIONLIMIT THEOREM

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 940 - 948
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Erdös, P. and Rényi, A. (1961) On a classical problem of probability theory. Magy. Tud. Akad. Mat. Kutató Int. Közl. 6, 215–220.Google Scholar
Holst, L. (1986) On birthday, collectors' occupancy and other classical urn problems. Internat. Statist. Rev. 54, 15–27.CrossRefGoogle Scholar
Johnson, N. L. and Kotz, S. (1977) Urn Models and Their Applications. Wiley, New York.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar