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Ordering properties of order statistics from random variables of Archimedean copulas with applications

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  • Li, Xiaohu
  • Fang, Rui

Abstract

Ordering properties on order statistics from heterogeneous observations have been paid lots of attention. This article devotes to investigating the ordering properties on order statistics from statistically dependent observations. We build the likelihood ratio order and the (reversed) hazard rate order of the extremal values and their adjacent order statistics. Also, some applications of our comparison results in TTE model and its dual version, auction theory and k-out-of-n reliability systems are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:304-320
    DOI: 10.1016/j.jmva.2014.09.016
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    References listed on IDEAS

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    1. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    2. Li, Xiaohu & Da, Gaofeng, 2010. "Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1016-1025, April.
    3. Mark Y. An & Bent Jesper Christensen & Nabanita Datta Gupta, 2004. "Multivariate mixed proportional hazard modelling of the joint retirement of married couples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(6), pages 687-704.
    4. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    Citations

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    Cited by:

    1. Longxiang Fang & Wenyu Huang, 2020. "Inequalities for Gaussian random variables under Archimedean copula dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 617-625, July.
    2. Longxiang Fang & Narayanaswamy Balakrishnan & Wenyu Huang & Shuai Zhang, 2023. "Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 99-112, February.
    3. Barmalzan, Ghobad & Akrami, Abbas & Balakrishnan, Narayanaswamy, 2020. "Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 341-352.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Enrique de Amo & María del Rosario Rodríguez-Griñolo & Manuel Úbeda-Flores, 2024. "Directional Dependence Orders of Random Vectors," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    11. 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).
    12. Li, Chen & Li, Xiaohu, 2021. "On stochastic dependence in residual lifetime and inactivity time with some applications," Statistics & Probability Letters, Elsevier, vol. 177(C).

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