Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are c...Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid grade correlation coefficients, and there exist linear Spearman compatible non-Bernoulli mixture trivariate copulas, one can ask when there exists at all a trivariate copula with given linear Spearman marginal copulas. Based on a known concordance ordering compatibility criterion, a set of grade correlation inequalities, which must necessarily be satisfied for compatibility, is derived. The existence question for trivariate copulas with compatible linear Spearman marginal copulas is settled in the main result, which states that this set of inequalities is also sufficient for compatibility. The constructive proof makes use of two new classes of trivariate copulas that are obtained from the Bernoulli mixture trivariate copulas through a natural parametric extension. Finally, the obtained classes of trivariate copulas are compared with another class that contains as special case some trivariate copulas with linear Spearman marginal copulas. Since the latter class is incompatible with some type of linear Spearman copulas, the new classes of trivariate copulas build a richer class in this respect. Moreover, in contrast to the mentioned class, which requires in general 11 different elementary copulas in the defining convex linear combination, the new classes require at most five of them, which results in a more parsimonious parametric modelling.展开更多
This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under m...This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.展开更多
文摘Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid grade correlation coefficients, and there exist linear Spearman compatible non-Bernoulli mixture trivariate copulas, one can ask when there exists at all a trivariate copula with given linear Spearman marginal copulas. Based on a known concordance ordering compatibility criterion, a set of grade correlation inequalities, which must necessarily be satisfied for compatibility, is derived. The existence question for trivariate copulas with compatible linear Spearman marginal copulas is settled in the main result, which states that this set of inequalities is also sufficient for compatibility. The constructive proof makes use of two new classes of trivariate copulas that are obtained from the Bernoulli mixture trivariate copulas through a natural parametric extension. Finally, the obtained classes of trivariate copulas are compared with another class that contains as special case some trivariate copulas with linear Spearman marginal copulas. Since the latter class is incompatible with some type of linear Spearman copulas, the new classes of trivariate copulas build a richer class in this respect. Moreover, in contrast to the mentioned class, which requires in general 11 different elementary copulas in the defining convex linear combination, the new classes require at most five of them, which results in a more parsimonious parametric modelling.
基金Shu Li and Jianfeng Wang are supported by NSFC(No.11971247)Jianfeng Wang is also supported by Special Fund for Taishan Scholars ProjectZoran Stanic is supported by the Science Fund of the Republic of Serbia(No.7749676:-SCSG-ctct)
基金This research is partly supported by National Outstanding Young Investigator Grant(70225005) of National Natural Science Foundation of China and the Project(70471088) of National Natural Science Foundation of China.
文摘This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.
