Functions operating on multivariate distribution and survival functions — With applications to classical mean-values and to copulas

摘要

Functions operating on multivariate distribution and survival functions are characterized, based on a theorem of Morillas, for which a new proof is presented. These results are applied to determine those classical mean values on [0, 1]n which are distribution functions of probability measures on [0, 1]n. As it turns out, the arithmetic mean plays a universal rôle for the characterization of distribution as well as survival functions. Another consequence is a far reaching generalization of Kimberling’s theorem, tightly connected to Archimedean copulas.