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Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials

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  • Serkan Eryilmaz

    (Atilim University)

Abstract

A new scheme-distribution-based representation is presented for the cumulative distribution function of the number of success runs of length k in a sequence of exchangeable binary trials. By utilizing this new representation, some stochastic ordering results are obtained to compare success runs. The results are illustrated for beta-binomial distributions of order k.

Suggested Citation

  • Serkan Eryilmaz, 2018. "Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 563-573, June.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9576-1
    DOI: 10.1007/s11009-017-9576-1
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    References listed on IDEAS

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    1. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.
    2. M. V. Koutras & S. Bersimis & P. E. Maravelakis, 2007. "Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 207-224, June.
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    4. Frosso Makri & Andreas Philippou, 2005. "On binomial and circular binomial distributions of orderk forl-overlapping success runs of lengthk," Statistical Papers, Springer, vol. 46(3), pages 411-432, July.
    5. Koutras, M. V. & Alexandrou, V. A., 1997. "Non-parametric randomness tests based on success runs of fixed length," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 393-404, April.
    6. Lou, W. Y. Wendy, 2003. "The exact distribution of the k-tuple statistic for sequence homology," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 51-59, January.
    7. Demetrios Antzoulakos & Stathis Chadjiconstantinidis, 2001. "Distributions of Numbers of Success Runs of Fixed Length in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 599-619, September.
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    Cited by:

    1. Boutsikas V. Michael & Vaggelatou Eutichia, 2020. "On the Distribution of the Number of Success Runs in a Continuous Time Markov Chain," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 969-993, September.

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