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Joint distribution of run statistics in partially exchangeable processes

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  • EryIlmaz, Serkan

Abstract

Let {Xi}i>=1 be an infinite sequence of recurrent partially exchangeable random variables with two possible outcomes as either "1" (success) or "0" (failure). In this paper we obtain the joint distribution of success and failure run statistics in {Xi}i>=1. The results can be used to obtain the joint distribution of runs in ordinary Markov chains, exchangeable and independent sequences.

Suggested Citation

  • EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:163-168
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    References listed on IDEAS

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    1. 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.
    2. Peng, Hanxiang & Dang, Xin & Wang, Xueqin, 2010. "The distribution of partially exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 932-938, June.
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    Cited by:

    1. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
    2. Frosso S. Makri & Zaharias M. Psillakis, 2016. "On runs of ones defined on a q-sequence of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 579-602, July.
    3. Makri, Frosso S. & Psillakis, Zaharias M. & Arapis, Anastasios N., 2015. "Length of the minimum sequence containing repeats of success runs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 28-37.
    4. Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
    5. Frosso Makri & Zaharias Psillakis, 2013. "Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes," Statistical Papers, Springer, vol. 54(3), pages 783-806, August.
    6. Anastasios N. Arapis & Frosso S. Makri & Zaharias M. Psillakis, 2017. "Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    7. Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
    8. Serkan Eryilmaz, 2014. "On Distributions of Runs in the Compound Binomial Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 149-159, March.

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