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Stochastic somparisons of order statistics from scaled and interdependent random variables

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Listed:
  • Chen Li

    (Xiamen University)

  • Rui Fang

    (Shantou University)

  • Xiaohu Li

    (Stevens Institute of Technology)

Abstract

This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:5:d:10.1007_s00184-015-0567-3
    DOI: 10.1007/s00184-015-0567-3
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    References listed on IDEAS

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    1. Jorge Navarro & Fabio Spizzichino, 2010. "Comparisons of series and parallel systems with components sharing the same copula," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(6), pages 775-791, November.
    2. Li, Chen & Li, Xiaohu, 2015. "Likelihood ratio order of sample minimum from heterogeneous Weibull random variables," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 46-53.
    3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, September.
    4. 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.
    5. Rezapour, Mohsen & Alamatsaz, Mohammad Hossein, 2014. "Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 240-251.
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    Citations

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    Cited by:

    1. Li, Chen & Li, Xiaohu, 2019. "Hazard rate and reversed hazard rate orders on extremes of heterogeneous and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 104-111.
    2. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    3. Ariyafar, Saeed & Tata, Mahbanoo & Rezapour, Mohsen & Madadi, Mohsen, 2020. "Comparison of aggregation, minimum and maximum of two risky portfolios with dependent claims," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    4. Jiandong Zhang & Rongfang Yan & Yiying Zhang, 2023. "Reliability analysis of fail-safe systems with heterogeneous and dependent components subject to random shocks," Journal of Risk and Reliability, , vol. 237(6), pages 1073-1087, December.
    5. Nil Kamal Hazra & Mithu Rani Kuiti & Maxim Finkelstein & Asok K. Nanda, 2018. "On stochastic comparisons of minimum order statistics from the location–scale family of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 105-123, February.
    6. 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.
    7. Mesfioui Mhamed & Trufin Julien, 2021. "Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors," Dependence Modeling, De Gruyter, vol. 9(1), pages 385-393, January.
    8. Sangita Das & Suchandan Kayal, 2020. "Ordering extremes of exponentiated location-scale models with dependent and heterogeneous random samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 869-893, November.
    9. Junrui Wang & Rongfang Yan & Bin Lu, 2020. "Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components," Mathematics, MDPI, vol. 8(4), pages 1-18, March.
    10. Hazra, Nil Kamal & Kuiti, Mithu Rani & Finkelstein, Maxim & Nanda, Asok K., 2017. "On stochastic comparisons of maximum order statistics from the location-scale family of distributions," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 31-41.

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