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Coupon Collector Problem with Reset Button

Author

Listed:
  • Jelena Jocković

    (Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Bojana Todić

    (Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

Abstract

We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection that has already been drawn. For the case where standard coupons have unequal probabilities of being drawn, we obtain the distribution of the waiting time until the end of the collection process. For the case where standard coupons have equal probabilities, we derive a simple formula for the expected waiting time in terms of the beta function, and discuss the asymptotic properties of this expected waiting time, when the number of standard coupons tends toward infinity.

Suggested Citation

  • Jelena Jocković & Bojana Todić, 2024. "Coupon Collector Problem with Reset Button," Mathematics, MDPI, vol. 12(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:239-:d:1317433
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    References listed on IDEAS

    as
    1. Kim, Bara & Kim, Jeongsim, 2019. "Sooner waiting time problems in a sequence of multi-state trials with random rewards," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 171-179.
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