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AIMS Mathematics

2026, Volume 11, Issue 7: 19739-19748. doi: 10.3934/math.2026800
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Generalized analysis of the coupon collector problem with reset button

  • 1.
    Department of Applied Mathematics, College of Science, China Agricultural University, Beijing 100083, China
  • 2.
    Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeollabuk-do 54896, South Korea
  • Published: 06 July 2026

  • MSC : 60C05, 60G50

  • In this paper, we study a generalized version of the coupon collector problem that includes a reset button, which restarts the collection process when it is drawn. We derive an explicit formula for the expected waiting time to collect all distinct coupons in the general case where standard coupons are drawn with arbitrary probabilities. Using this result, we reprove the recent expected waiting time formula by Jocković and Todić in [8] for the case where standard coupons have equal probabilities, which is expressed in terms of the beta function.

    Citation: Yan Li, Cancan Dai, Daeyeoul Kim. Generalized analysis of the coupon collector problem with reset button[J]. AIMS Mathematics, 2026, 11(7): 19739-19748. doi: 10.3934/math.2026800

    Related Papers:

  • In this paper, we study a generalized version of the coupon collector problem that includes a reset button, which restarts the collection process when it is drawn. We derive an explicit formula for the expected waiting time to collect all distinct coupons in the general case where standard coupons are drawn with arbitrary probabilities. Using this result, we reprove the recent expected waiting time formula by Jocković and Todić in [8] for the case where standard coupons have equal probabilities, which is expressed in terms of the beta function.



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