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Length of the minimum sequence containing repeats of success runs

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  • Makri, Frosso S.
  • Psillakis, Zaharias M.
  • Arapis, Anastasios N.

Abstract

Let a sequence of binary (zero–one or failure–success) trials ordered on a line. We consider runs of successes of length at least equal to a fixed number. The statistics denoting the size (length) as well as the starting and ending positions of the minimum subsequence containing all such runs are defined and studied. The study concerns with conditional probability distributions of these and other related statistics given that the number of such success runs in the sequence is at least equal to two. Numerical examples illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:28-37
    DOI: 10.1016/j.spl.2014.09.003
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    References listed on IDEAS

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    1. Makri, Frosso S., 2011. "Minimum and maximum distances between failures in binary sequences," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 402-410, March.
    2. 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.
    3. EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.
    4. 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.
    5. 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.
    6. Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.
    7. 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.
    8. 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.
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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. 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.
    3. 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.
    4. 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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