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Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks

Author

Listed:
  • Ebrahim Amini-Seresht

    (Bu-Ali Sina University)

  • Ebrahim Nasiroleslami

    (Bu-Ali Sina University)

  • Narayanaswamy Balakrishnan

    (McMaster University)

Abstract

In this paper, we consider two k-out-of-n systems comprising heterogeneous dependent components under random shocks, with an Archimedean copula. We then provide sufficient conditions on the distributions of components’ lifetimes and the generator of the Archimedean copula and on the random shocks for comparing the lifetimes of two systems with respect to the usual stochastic order. Finally, we present some examples to illustrate the established results.

Suggested Citation

  • Ebrahim Amini-Seresht & Ebrahim Nasiroleslami & Narayanaswamy Balakrishnan, 2024. "Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(2), pages 133-153, February.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:2:d:10.1007_s00184-023-00905-5
    DOI: 10.1007/s00184-023-00905-5
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Zhao, Peng, 2013. "Hazard rate comparison of parallel systems with heterogeneous gamma components," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 153-160.
    2. Narayanaswamy Balakrishnan & Yiying Zhang & Peng Zhao, 2018. "Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(1), pages 23-41, January.
    3. Ebrahim Amini-Seresht & Jianfei Qiao & Yiying Zhang & Peng Zhao, 2016. "On the skewness of order statistics in multiple-outlier PHR models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 817-836, October.
    4. M. Mesfioui & M. Kayid & S. Izadkhah, 2017. "Stochastic comparisons of order statistics from heterogeneous random variables with Archimedean copula," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 749-766, November.
    5. Li, Xiaohu & Fang, Rui, 2015. "Ordering properties of order statistics from random variables of Archimedean copulas with applications," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 304-320.
    6. Nuria Torrado & Jorge Navarro, 2021. "Ranking the extreme claim amounts in dependent individual risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(3), pages 218-247, March.
    7. Chen Li & Rui Fang & Xiaohu Li, 2016. "Stochastic somparisons of order statistics from scaled and interdependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 553-578, July.
    8. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.
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