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Sooner waiting time problems in a sequence of multi-state trials with random rewards

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  • Kim, Bara
  • Kim, Jeongsim

Abstract

We investigate sooner waiting time problems in a sequence of independent multi-state trials with random rewards. Our result generalizes the sooner waiting time problems of Eryilmaz, Gong, and Xie (2016) for a sequence of trinary trials with random rewards to the case of multi-state trials. This generalization is obtained through the analysis of a Markov chain with a special transition structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:171-179
    DOI: 10.1016/j.spl.2019.06.017
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    References listed on IDEAS

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    1. Kim, Sungsu & Park, Chongjin & Oh, Jungtaek, 2013. "On waiting time distribution of runs of ones or zeros in a Bernoulli sequence," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 339-344.
    2. Qing Han & Sigeo Aki, 1999. "Joint Distributions of Runs in a Sequence of Multi-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 419-447, September.
    3. Sigeo Aki & Katuomi Hirano, 1999. "Sooner and Later Waiting Time Problems for Runs in Markov Dependent Bivariate Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 17-29, March.
    4. Ebneshahrashoob, M. & Sobel, Milton, 1990. "Sooner and later waiting time problems for Bernoulli trials: frequency and run quotas," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 5-11, January.
    5. Eryilmaz, Serkan & Gong, Min & Xie, Min, 2016. "Generalized sooner waiting time problems in a sequence of trinary trials," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 70-78.
    6. Balasubramanian, K. & Viveros, R. & Balakrishnan, N., 1993. "Sooner and later waiting time problems for Markovian Bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 153-161, September.
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    Cited by:

    1. Jelena Jocković & Bojana Todić, 2024. "Coupon Collector Problem with Reset Button," Mathematics, MDPI, vol. 12(2), pages 1-12, January.
    2. Bara Kim & Jeongsim Kim & Jerim Kim, 2020. "Waiting Time Problems for Patterns in a Sequence of Multi-State Trials," Mathematics, MDPI, vol. 8(11), pages 1-16, October.

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