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Approximation for counts of head runs

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Abstract

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein’s method and coupling.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Mei Zhang

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  1. Mei Zhang
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Correspondence to Mei Zhang.

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Zhang, M. Approximation for counts of head runs. Sci. China Math. 54, 311–324 (2011). https://doi.org/10.1007/s11425-010-4104-6

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  • DOI: https://doi.org/10.1007/s11425-010-4104-6

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