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On ℓ-overlapping Runs of Ones of Length k in Sequences of Independent Binary Random Variables

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  • Frosso S. Makri
  • Zaharias M. Psillakis

Abstract

Consider a finite sequence of independent binary (zero-one) random variables ordered on a line or on a circle. The number of the ℓ-overlapping runs of ones of a fixed length k is studied for both types of the concerned ordering. Recurrences for the exact probability mass functions for these numbers are obtained via simple probabilistic arguments. Exact closed formulae, for the mean and variance of the studied numbers are obtained via their representations through properly defined indicators. Two application case studies, concerning record sequences and reliability of consecutive systems, clarify further the theoretical results.

Suggested Citation

  • Frosso S. Makri & Zaharias M. Psillakis, 2015. "On ℓ-overlapping Runs of Ones of Length k in Sequences of Independent Binary Random Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3865-3884, September.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:18:p:3865-3884
    DOI: 10.1080/03610926.2013.788717
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    Cited by:

    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. 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.
    3. 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.

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