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The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials

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Abstract

The total number of successes in success runs of length greater than or equal to k in a sequence of n two-state trials is a statistic that has been broadly used in statistics and probability. For Bernoulli trials with k equal to one, this statistic has been shown to have binomial and normal distributions as exact and limiting distributions, respectively. For the case of Markov-dependent two-state trials with k greater than one, its exact and limiting distributions have never been considered in the literature. In this article, the finite Markov chain imbedding technique and the invariance principle are used to obtain, in general, the exact and limiting distributions of this statistic under Markov dependence, respectively. Numerical examples are given to illustrate the theoretical results.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2

    James C. Fu

  2. Department of Public Health Sciences, University of Toronto, Toronto, Ontario, Canada, M5S 1A8

    W. Y. Wendy Lou

  3. Department of Statistics and Applied Probability, National University of Singapore, Singapore, 119260, Singapore

    Zhi-Dong Bai

  4. Biometrics, Organon, Inc., West Orange, NJ 07052, U.S.A

    Gang Li

Authors
  1. James C. Fu
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  2. W. Y. Wendy Lou
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  3. Zhi-Dong Bai
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  4. Gang Li
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Fu, J.C., Lou, W.Y.W., Bai, ZD. et al. The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials. Annals of the Institute of Statistical Mathematics 54, 719–730 (2002). https://doi.org/10.1023/A:1022451015903

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  • DOI: https://doi.org/10.1023/A:1022451015903

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