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Number of occurrences of subpattern until the first appearance of a pattern and geometric distribution

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  • Hirano, Katuomi
  • Aki, Sigeo

Abstract

The exact distribution of the number of occurrences of subpattern of a specified length or larger until the first occurrence of a pattern is studied in a sequence of multi-state independent trials. If the pattern and the subpattern of the specified lengths, respectively, satisfy a condition and the number of occurrences of subpattern is appropriately enumerated, the distribution follows a geometric distribution. Further, the problem is studied in the sequence of mth order Markov chains. If the specified length of the subpattern is not less than m, then the corresponding distribution is still a geometric distribution.

Suggested Citation

  • Hirano, Katuomi & Aki, Sigeo, 2003. "Number of occurrences of subpattern until the first appearance of a pattern and geometric distribution," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 259-262, November.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:3:p:259-262
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    References listed on IDEAS

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    1. Sigeo Aki & Katuomi Hirano, 2000. "Numbers of Success-Runs of Specified Length Until Certain Stopping Time Rules and Generalized Binomial Distributions of Order k," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 767-777, December.
    2. Sigeo Aki & Katuomi Hirano, 1995. "Joint distributions of numbers of success-runs and failures until the first consecutivek successes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 225-235, June.
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    Cited by:

    1. Pozdnyakov, Vladimir, 2008. "On occurrence of patterns in Markov chains: Method of gambling teams," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2762-2767, November.
    2. Kiyoshi Inoue & Sigeo Aki, 2009. "On waiting time distributions associated with compound patterns in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 499-516, June.

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