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The distribution of increasing 2-sequences in random permutations of arbitrary multi-sets

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  • Johnson, Brad C.

Abstract

The distribution of increasing 2-sequences in random permutations of the first n integers is generalized to random permutations of arbitrary multi-sets using a finite Markov chain embedding technique. A numerical example is provided to aid in understanding and some applications are briefly discussed.

Suggested Citation

  • Johnson, Brad C., 2002. "The distribution of increasing 2-sequences in random permutations of arbitrary multi-sets," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 67-74, August.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:1:p:67-74
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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. 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.
    4. James Fu & W.Y. Lou, 2000. "Joint Distribution of Rises and Falls," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 415-425, September.
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    Cited by:

    1. Lou, W.Y. Wendy & Fu, James C., 2007. "On exact Type I and Type II errors of Cochran's test," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1282-1287, July.
    2. James C. Fu, 2012. "On the Distribution of the Number of Occurrences of an Order-Preserving Pattern of Length Three in a Random Permutation," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 831-842, September.

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