Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE lif...Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE life distributions isessentially a series system composed of components with multivariate exponential lifedistributions. Also, it is proved that for cold standby systems composed of componentswith multivariate NBU life distributions, all but oue of the components are degenerateat zero while the remaining one is exponential. In addition, several equivalent char-acterizations of multivariate exponential distribution are provided in the multivariateHNBUE life distribution class which include many existing results as special cases.展开更多
This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a s...This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems;the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.展开更多
Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate tr...Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate truncated normal and multivariate truncated t distributions.We derive statistical properties of the truncated elliptical distributions.Applications of our results establish new properties of the multivariate truncated slash and multivariate truncated power exponential distributions.展开更多
基金This work is supported by the Natural Science Foundation of the Jiangsu Provincial Education Commission.
文摘Structures of monotone systems and cold standby systems with exponen-tial life distributions and dependent components are studied. It is shown that a mono-tone system composed of components with multivariate HNBUE life distributions isessentially a series system composed of components with multivariate exponential lifedistributions. Also, it is proved that for cold standby systems composed of componentswith multivariate NBU life distributions, all but oue of the components are degenerateat zero while the remaining one is exponential. In addition, several equivalent char-acterizations of multivariate exponential distribution are provided in the multivariateHNBUE life distribution class which include many existing results as special cases.
文摘This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems;the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.
基金Conselho Nacional de Desenvolvi-mento Cientifico e Tecnologico-CNPq(Grant No.305963-2018-0).
文摘Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate truncated normal and multivariate truncated t distributions.We derive statistical properties of the truncated elliptical distributions.Applications of our results establish new properties of the multivariate truncated slash and multivariate truncated power exponential distributions.
