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On runs of ones defined on a q-sequence of binary trials

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  • Frosso S. Makri

    (University of Patras)

  • Zaharias M. Psillakis

    (University of Patras)

Abstract

In a sequence of n binary ( $$0{-}1$$ 0 - 1 ) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k, $$1\le k\le n$$ 1 ≤ k ≤ n . Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:5:d:10.1007_s00184-015-0568-2
    DOI: 10.1007/s00184-015-0568-2
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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. S. Aki & K. Hirano, 1989. "Estimation of parameters in the discrete distributions of order k," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 47-61, March.
    3. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
    4. Sevcan Demir & Serkan Eryılmaz, 2010. "Run statistics in a sequence of arbitrarily dependent binary trials," Statistical Papers, Springer, vol. 51(4), pages 959-973, December.
    5. EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.
    6. 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.
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    Cited by:

    1. Eryilmaz, Serkan, 2018. "On success runs in a sequence of dependent trials with a change point," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 91-98.
    2. 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.
    3. 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.
    4. Spiros D. Dafnis & Frosso S. Makri, 2023. "Distributions Related to Weak Runs With a Minimum and a Maximum Number of Successes: A Unified Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.

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