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Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components

Author

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  • Chen Li

    (Tianjin University of Commerce)

  • Xiaohu Li

    (Stevens Institute of Technology)

Abstract

This paper investigates sufficient conditions for preservation property of the increasing convex order and the increasing concave order under the taking of maximum and minimum of statistically dependent random variables, respectively. As applications, we develop the preservation of NBUC and NBU(2) aging properties respectively under the parallel and series systems of components with statistically dependent lifetimes. Some copulas are presented as illustrations on statistical dependence structure satisfying the sufficient condition as well.

Suggested Citation

  • Chen Li & Xiaohu Li, 2018. "Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 445-464, May.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:4:d:10.1007_s00184-018-0651-6
    DOI: 10.1007/s00184-018-0651-6
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    References listed on IDEAS

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    1. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.
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    Cited by:

    1. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    2. Antonia Castaño-Martínez & Gema Pigueiras & Georgios Psarrakos & Miguel A. Sordo, 2020. "Increasing concave orderings of linear combinations of order statistics with applications to social welfare," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 699-712, August.
    3. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.

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