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Distribution of Patterns of Constrained Length in Binary Sequences

Author

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  • Frosso S. Makri

    (University of Patras)

  • Zaharias M. Psillakis

    (University of Patras)

Abstract

On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.

Suggested Citation

  • Frosso S. Makri & Zaharias M. Psillakis, 2023. "Distribution of Patterns of Constrained Length in Binary Sequences," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-15, December.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:4:d:10.1007_s11009-023-10068-5
    DOI: 10.1007/s11009-023-10068-5
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    References listed on IDEAS

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    1. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    2. 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.
    3. Spiros D. Dafnis & Frosso S. Makri & Markos V. Koutras, 2021. "Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 165-185, March.
    4. Gera, Amos E., 2018. "Simultaneous demonstration tests involving sparse failures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 26-31.
    5. F.S. Makri & Z.M. Psillakis, 2017. "On Limited Length Binary Strings with an Application in Statistical Control," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 1-6, February.
    Full references (including those not matched with items on IDEAS)

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