Dynamic linkages for multivariate distributions with given nonoverlapping multivariate marginals

One of the most useful tools for handling multivariate distributions with g iven univariate marginals is the copula function. Using it, any multivariat e distribution function can be represented in a way that emphasizes the sep arate roles of the marginals and of the dependence structure. Li et al. (19 96) introduced an analogous tool, called linkage. which is useful for handl ing multivariate distributions with given multivariate marginals. The goal of the present paper is to introduce a new hind of linkage, called the dyna mic linkage, which can usefully handle multivariate life distributions (tha t is distributions of non-negative random variables) by taking advantage of the time dynamics of the underlying lifetimes. Like the linkages of Li et al. (1996), the new dynamic linkage can be used for the study of multivaria te distributions with given multivariate marginals by emphasizing the separ ate roles of the dependence structure among the given multivariate marginal s and the dependence structure within each of the nonoverlapping marginals. Preservation of some setwise positive dependence properties, from the dyna mic linkage function L to the joint distribution F and vice versa. are stud ied. When two different distribution functions are associated with the same dynamic linkage (that is. have the same setwise dependence structure) we s how that the cumulative hazard order among the corresponding multivariate m arginal distributions implies an overall stochastic dominance between the t wo underlying distribution functions. (C) 1999 Academic Press.