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Convergence in Mean for Double Arrays of M-Pairwise Negatively Dependent Random Variables

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Abstract

This paper proves a theorem on convergence in mean of order p for double arrays of M-pairwise negatively dependent random variables, where \(1 \le p < 2\). The main result extends some results in Thành (Int J Math Math Sci 27(8):1317–1320, 2005) and Hong and Hwang (Int J Math Math Sci 22(1):171–177, 1999). The proof is based on the von Bahr–Esseen inequality for M-pairwise negatively dependent random variables. The sharpness of the result is illustrated by two examples.

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Acknowledgements

The authors express their thanks to the referees for their helpful comments and suggestions. This work belongs to the project in 2022 funded by Ho Chi Minh City University of Technology and Education, Vietnam.

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Authors and Affiliations

  1. Department of Applied Sciences, HCMC University of Technology and Education, 01 Vo Van Ngan Street, Thu Duc City, Ho Chi Minh City, Vietnam

    Vo Thi Van Anh & Nguyen Ngoc Tu

  2. Department of Mathematics, Vinh University, 182 Le Duan, Vinh City, Nghe An, Vietnam

    Nguyen Thi Ngoc Anh

  3. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

    Nguyen Thi Thanh Hien

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  1. Vo Thi Van Anh
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  2. Nguyen Thi Ngoc Anh
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  3. Nguyen Thi Thanh Hien
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  4. Nguyen Ngoc Tu
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Correspondence to Nguyen Ngoc Tu.

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Communicated by See Keong Lee.

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Van Anh, V.T., Anh, N.T.N., Hien, N.T.T. et al. Convergence in Mean for Double Arrays of M-Pairwise Negatively Dependent Random Variables. Bull. Malays. Math. Sci. Soc. 45, 1507–1520 (2022). https://doi.org/10.1007/s40840-022-01274-4

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  • DOI: https://doi.org/10.1007/s40840-022-01274-4

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