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Some New Bivariate Properties and Characterizations Under Archimedean Copula

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  • Qingyuan Guan

    (School of Mathematics and Computer Science, Wuyi University, Wuyishan 354300, China
    Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions, Wuyishan 354300, China
    Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry, Wuyishan 354300, China)

  • Peihua Jiang

    (School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000, China)

  • Guangyu Liu

    (School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000, China)

Abstract

This paper considers comparing properties and characterizations of the bivariate functions under Archimedean copula. It is shown that some results of the usual stochastic order for the bivariate functions in the independent case are generalized to the Archimedean copula-linked dependent case, and we also derive some characterizations of different bivariate functions composed by Archimedean copula-linked dependent random variables. These results generalize some existing results in the literature and bring conclusions closer to reality. Two applications in scheduling problems are also provided to illustrate the main results.

Suggested Citation

  • Qingyuan Guan & Peihua Jiang & Guangyu Liu, 2024. "Some New Bivariate Properties and Characterizations Under Archimedean Copula," Mathematics, MDPI, vol. 12(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3714-:d:1530277
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    References listed on IDEAS

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    1. 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.
    2. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
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    4. Subhash C. Kochar & Nuria Torrado, 2015. "On Stochastic Comparisons of Largest Order Statistics in the Scale Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(19), pages 4132-4143, October.
    5. 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).
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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