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Joint distributions of numbers of runs of specified lengths on directed trees

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  • Kiyoshi Inoue

    (Seikei University)

  • Sigeo Aki

    (Kansai University)

Abstract

In this paper, we consider exact joint distributions of numbers of success runs of specified lengths on a Markov directed tree under $$\ell $$ ℓ -overlapping enumeration schemes. Methods for deriving the probability generating functions of the joint distribution are presented. We extend the exact distribution theory of runs based on sequences to runs based on directed trees. Some numerical results for the run statistics are given in order to illustrate the computational aspects and the feasibility of our theoretical results. The reliability systems and lifetime distributions are considered. Our general results are applied to reliability systems and lifetime distributions. Finally, we discuss parametric estimation problems based on the lifetimes of the systems.

Suggested Citation

  • Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0762-y
    DOI: 10.1007/s00362-016-0762-y
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    References listed on IDEAS

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    2. Inoue, Kiyoshi & Aki, Sigeo, 2010. "On the conditional and unconditional distributions of the number of success runs on a circle with applications," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 874-885, May.
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    13. Kiyoshi Inoue & Sigeo Aki, 2005. "Joint distributions of numbers of success runs of specified lengths in linear and circular sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 353-368, June.
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