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Volume 12
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Article

Some New Bivariate Properties and Characterizations Under Archimedean Copula

by
Qingyuan Guan
1,2,3,
Peihua Jiang
4,* and
Guangyu Liu
4
1
School of Mathematics and Computer Science, Wuyi University, Wuyishan 354300, China
2
Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions, Wuyishan 354300, China
3
Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry, Wuyishan 354300, China
4
School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(23), 3714; https://doi.org/10.3390/math12233714 (registering DOI)
Submission received: 30 October 2024 / Revised: 21 November 2024 / Accepted: 22 November 2024 / Published: 26 November 2024
(This article belongs to the Special Issue Research Progress of Probability Statistics)
Versions Notes

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.
Keywords: usual stochastic order; characterizations; bivariate functions; Archimedean copula usual stochastic order; characterizations; bivariate functions; Archimedean copula

Share and Cite

MDPI and ACS Style

Guan, Q.; Jiang, P.; Liu, G. Some New Bivariate Properties and Characterizations Under Archimedean Copula. Mathematics 2024, 12, 3714. https://doi.org/10.3390/math12233714

AMA Style

Guan Q, Jiang P, Liu G. Some New Bivariate Properties and Characterizations Under Archimedean Copula. Mathematics. 2024; 12(23):3714. https://doi.org/10.3390/math12233714

Chicago/Turabian Style

Guan, Qingyuan, Peihua Jiang, and Guangyu Liu. 2024. "Some New Bivariate Properties and Characterizations Under Archimedean Copula" Mathematics 12, no. 23: 3714. https://doi.org/10.3390/math12233714

APA Style

Guan, Q., Jiang, P., & Liu, G. (2024). Some New Bivariate Properties and Characterizations Under Archimedean Copula. Mathematics, 12(23), 3714. https://doi.org/10.3390/math12233714

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