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Limiting Behaviors for Longest Consecutive Switches in an IID Bernoulli Sequence

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Abstract

In this paper we mainly discuss lower and upper bounds for the length of longest consecutive switches in IID Bernoulli sequences. This work is an extension of results for longest consecutive switches in unbiased coin-tossing, and might be applied to reliability theory, biology, quality control, pattern recognition, finance, etc.

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Acknowledgements

We thank the two referees for helpful comments and useful suggestions, which helped to improve the presentation of this note. We also thank Prof. Ze-Chun Hu for helpful discussion.

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610065, P.R. China

    Chen Xu Hao & Ting Ma

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  1. Chen Xu Hao
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  2. Ting Ma
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Correspondence to Ting Ma.

Additional information

Supported by the National National Science Foundation of China (Grant Nos. 12101429, 12171335), the Science Development Project of Sichuan University (Grant No. 2020SCUNL201) and the Fundamental Research Funds for the Central Universities of China

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Hao, C.X., Ma, T. Limiting Behaviors for Longest Consecutive Switches in an IID Bernoulli Sequence. Acta. Math. Sin.-English Ser. 39, 1138–1146 (2023). https://doi.org/10.1007/s10114-023-1355-z

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  • DOI: https://doi.org/10.1007/s10114-023-1355-z

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