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A Survey of the Coupon Collector’s Problem with Random Sample Sizes

Author

Listed:
  • John E. Kobza

    (Texas Tech University)

  • Sheldon H. Jacobson

    (University of Illinois)

  • Diane E. Vaughan

    (Los Alamos National Laboratory)

Abstract

This paper surveys the coupon collector’s waiting time problem with random sample sizes and equally likely balls. Consider an urn containing m red balls. For each draw, a random number of balls are removed from the urn. The group of removed balls is painted white and returned to the urn. Several approaches to addressing this problem are discussed, including a Markov chain approach to compute the distribution and expected value of the number of draws required for the urn to contain j white balls given that it currently contains i white balls. As a special case, E[N], the expected number of draws until all the balls are white given that all are currently red is also obtained.

Suggested Citation

  • John E. Kobza & Sheldon H. Jacobson & Diane E. Vaughan, 2007. "A Survey of the Coupon Collector’s Problem with Random Sample Sizes," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 573-584, December.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:4:d:10.1007_s11009-006-9013-3
    DOI: 10.1007/s11009-006-9013-3
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    References listed on IDEAS

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    1. Thierry Huillet & Servet Martinez, 2003. "Sampling from Finite Random Partitions," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 467-492, December.
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    Cited by:

    1. Brad C. Johnson & Thomas M. Sellke, 2010. "On the Number of i.i.d. Samples Required to Observe All of the Balls in an Urn," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 139-154, March.
    2. Shigeo Shioda, 2021. "Coupon Subset Collection Problem with Quotas," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1203-1235, December.
    3. Tamar Gadrich & Rachel Ravid, 2011. "The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 433-448, June.

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