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Distribution of the Number of Successes in Success Runs of Length at Least k in Higher-Order Markovian Sequences

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  • Donald E. K. Martin

    (Howard University
    US Bureau of the Census)

Abstract

We consider the distribution of the number of successes in success runs of length at least k in a binary sequence. One important application of this statistic is in the detection of tandem repeats among DNA sequence segments. In the literature, its distribution has been computed for independent sequences and Markovian sequences of order one. We extend these results to Markovian sequences of a general order. We also show that the statistic can be represented as a function of the number of overlapping success runs of lengths k and k + 1 in the sequence, and give immediate consequences of this representation.

Suggested Citation

  • Donald E. K. Martin, 2005. "Distribution of the Number of Successes in Success Runs of Length at Least k in Higher-Order Markovian Sequences," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 543-554, December.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:4:d:10.1007_s11009-005-5007-9
    DOI: 10.1007/s11009-005-5007-9
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    References listed on IDEAS

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    1. James Fu & W. Lou & Zhi-Dong Bai & Gang Li, 2002. "The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 719-730, December.
    2. 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. Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.

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