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Waiting time problem for an almost perfect match

Author

Listed:
  • Han, Qing
  • Hirano, Katuomi

Abstract

Given sequences of finite-state trials, an almost perfect match means that there exists at least k-1 matches between any subsequences of size k in each sequence. Let X1,X2,... be a sequence of {0,1}-valued Markov dependent random variables each resulting in either a match (Xi=1) or mismatch (Xi=0) for i=1,2,... . An explicit expression of the probability generating function of the waiting time for the first occurrence of an almost perfect match is derived. Numerical examples are also given.

Suggested Citation

  • Han, Qing & Hirano, Katuomi, 2003. "Waiting time problem for an almost perfect match," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 39-49, October.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:1:p:39-49
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    References listed on IDEAS

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    1. S. Robin & J.-J. Daudin, 2001. "Exact Distribution of the Distances between Any Occurrences of a Set of Words," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 895-905, December.
    2. Chang, C. J. & Fann, C. S. J. & Chou, W. C. & Lian, I. B., 2003. "On the tail probability of the longest well-matching run," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 267-274, July.
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    Cited by:

    1. Sotiris Bersimis & Markos V. Koutras & George K. Papadopoulos, 2014. "Waiting Time for an Almost Perfect Run and Applications in Statistical Process Control," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 207-222, March.
    2. Chang, Yung-Ming, 2005. "Distribution of waiting time until the rth occurrence of a compound pattern," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 29-38, November.

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