Please use this identifier to cite or link to this item: https://doi.org/10.1023/A:1022451015903
Title: The exact and limiting distributions for the number of successes in success runs within a sequence of Markov-dependent two-state trials
Authors: Fu, J.C.
Lou, W.Y.W.
Bai, Z.-D. 
Li, G.
Keywords: Finite Markov chain imbedding
Runs and patterns
Transition probability matrix
Issue Date: 2002
Citation: Fu, J.C., Lou, W.Y.W., Bai, Z.-D., Li, G. (2002). 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 (4) : 719-730. ScholarBank@NUS Repository. https://doi.org/10.1023/A:1022451015903
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.
Source Title: Annals of the Institute of Statistical Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/105419
ISSN: 00203157
DOI: 10.1023/A:1022451015903
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