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Uniform Cramér moderate deviations and Berry–Esseen bounds for superadditive bisexual branching processes in random environments

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Abstract

Let (Zn) be a superadditive bisexual branching process in an independent and identically distributed (i.i.d.) random environment ξ. We establish Cramér moderate deviations and Berry-Esseen bounds for log(Zn+n0=Zn0) uniformly in n0 ≥ 0. As an application of Cramér moderate deviation, we give the confidence interval of the parameter E log r1(ξ0) in terms of known population sizes Zn0, Zn+n0, and generation n, where r1(ξn) denotes the average number of mating units formed by the offspring of the same mating unit of generation n when the environment ξ is given.

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Authors and Affiliations

  1. Department of Applied Statistics, Hunan First Normal University, Changsha, 410205, Hunan, China

    Sheng Xiao

  2. Department of Statistics, Jinan University, Guangzhou, 510632, Guangdong, China

    Xiangdong Liu

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  1. Sheng Xiao
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  2. Xiangdong Liu
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Correspondence to Xiangdong Liu.

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This work is supported by National Natural Science Foundation of China (grant No. 12271062), Fundamental Research Funds for the Central University (grant No. 19JNLH09), Hunan Provincial Department of Education outstanding youth project, P.R. China (grant No. 23B0845).

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Xiao, S., Liu, X. Uniform Cramér moderate deviations and Berry–Esseen bounds for superadditive bisexual branching processes in random environments. Lith Math J (2024). https://doi.org/10.1007/s10986-024-09627-1

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  • DOI: https://doi.org/10.1007/s10986-024-09627-1

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