In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for t...In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.展开更多
This paper considers series and parallel systems comprising n components drawn from a heterogeneous population consisting of m different subpopulations.The components within each subpopulation are assumed to be depend...This paper considers series and parallel systems comprising n components drawn from a heterogeneous population consisting of m different subpopulations.The components within each subpopulation are assumed to be dependent,while the subpopulations are independent of each other.The authors also assume that the subpopulations have different Archimedean copulas for their dependence.Under this setup,the authors discuss the series and parallel systems reliability for three different cases,respectively.The authors use the theory of stochastic orders and majorization to establish the main results,and finally present some numerical examples to illustrate all the results established here.展开更多
基金Foundation item： Supported by the Scientific Research Common Program of Beijing Municipal Commission of Education of China（Km200611417009） Suppoted by the Natural Science Foundation of Fujian Province Education Department of China（JA05324）
文摘In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.
基金supported by the National Natural Science Foundation of China under Grant No.11971116the Anhui Provincial Natural Science Foundation under Grant No.1808085MA03the PhD research startup foundation of Anhui Normal University under Grant No.2014bsqdjj34。
文摘This paper considers series and parallel systems comprising n components drawn from a heterogeneous population consisting of m different subpopulations.The components within each subpopulation are assumed to be dependent,while the subpopulations are independent of each other.The authors also assume that the subpopulations have different Archimedean copulas for their dependence.Under this setup,the authors discuss the series and parallel systems reliability for three different cases,respectively.The authors use the theory of stochastic orders and majorization to establish the main results,and finally present some numerical examples to illustrate all the results established here.
