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Distribution of runs in a sequence of exchangeable multi-state trials

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  • EryIlmaz, Serkan

Abstract

Let {Xi}i>=1 be a an infinite sequence of exchangeable multi-state trials with m (m>=2) possible values. The exact distributions of runs, particularly the total number of runs, longest and shortest runs, in {Xi}i>=1 are derived. Applications associated with multi-color Pólya urn sampling scheme and statistical process control are also provided.

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  • EryIlmaz, Serkan, 2008. "Distribution of runs in a sequence of exchangeable multi-state trials," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1505-1513, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1505-1513
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    References listed on IDEAS

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    1. Vaggelatou, Eutichia, 2003. "On the length of the longest run in a multi-state Markov chain," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 211-221, April.
    2. C. Fu, James & Shmueli, Galit & Chang, Y. M., 2003. "A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 457-466, December.
    3. 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.
    4. Demetrios Antzoulakos & Andreas Philippou, 1997. "Probability Distribution Functions of Succession Quotas in the Case of Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 531-539, September.
    5. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
    6. Kong, Yong, 2006. "Distribution of Runs and Longest Runs: A New Generating Function Approach," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1253-1263, September.
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    Cited by:

    1. Kiyoshi Inoue, 2021. "On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1129-1153, September.
    2. Xian Zhao & Yanbo Song & Xiaoyue Wang & Zhiyue Lv, 2022. "Distributions of $$({k}_{1},{k}_{2},\dots ,{k}_{m})$$ ( k 1 , k 2 , ⋯ , k m ) -runs with Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2689-2702, December.
    3. EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.

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