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

Author

Listed:
  • 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. Miguel Sordo & Jorge Navarro & José Sarabia, 2014. "Distorted Lorenz curves: models and comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 761-780, April.
    2. 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.
    3. Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
    4. Nanda, Asok K. & Jain, Kanchan & Singh, Harshinder, 1998. "Preservation of some partial orderings under the formation of coherent systems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 123-131, August.
    5. Chen Li & Xiaohu Li, 2017. "Aging and ordering properties of multivariate lifetimes with Archimedean dependence structures," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 874-891, January.
    6. Li, Xiaohu & Li, Zehui & Jing, Bing-Yi, 2000. "Some results about the NBUC class of life distributions," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 229-237, February.
    7. Cai, Jun & Wei, Wei, 2012. "On the invariant properties of notions of positive dependence and copulas under increasing transformations," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 43-49.
    8. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.
    9. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
    10. Li, Yulin, 2004. "Closure of NBU(2) class under the formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 57-63, March.
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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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