Some New Bivariate Properties and Characterizations Under Archimedean Copula

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.