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On Finite Markov Chain Imbedding and Its Applications

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  • Tung-Lung Wu

    (University of Manitoba)

Abstract

The finite Markov Chain Imbedding technique has been successfully applied in various fields for finding the exact or approximate distributions of runs and patterns under independent and identically distributed or Markov dependent trials. In this paper, we derive a new recursive equation for distribution of scan statistic using the finite Markov chain imbedding technique. We also address the problem of obtaining transition probabilities of the imbedded Markov chain by introducing a notion termed Double Finite Markov Chain Imbedding where transition probabilities are obtained by using the finite Markov chain imbedding technique again. Applications for random permutation model in chemistry and coupon collector’s problem are given to illustrate our idea.

Suggested Citation

  • Tung-Lung Wu, 2013. "On Finite Markov Chain Imbedding and Its Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 453-465, June.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:2:d:10.1007_s11009-011-9268-1
    DOI: 10.1007/s11009-011-9268-1
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    References listed on IDEAS

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    1. James Fu, 1995. "Exact and limiting distributions of the number of successions in a random permutation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 435-446, September.
    2. Fu, James C. & Lou, W. Y. Wendy & Wang, Yueh-Jir, 1999. "On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 115-125, April.
    3. Brad C. Johnson & Thomas M. Sellke, 2010. "On the Number of i.i.d. Samples Required to Observe All of the Balls in an Urn," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 139-154, March.
    4. Yung-Ming Chang & Tung-Lung Wu, 2011. "On Average Run Lengths of Control Charts for Autocorrelated Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 419-431, June.
    5. Johnson, Brad C. & Fu, James C., 2000. "The distribution of increasing l-sequences in random permutations: a Markov chain approach," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 337-344, October.
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    Cited by:

    1. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).

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