Dependence by reverse regular rule
The paper announced above, Zbl 0621.62053, generalizes the bivariate positive dependence notions of the reviewer [J. Am. Stat. Assoc. 72, 642- 650 (1977; Zbl 0375.62092)] to the multivariate setting. It does this by requiring various iterated integrals of the density of a multivariate random vector to be totally positive of order 2. Some relations with other positive dependence concepts are discussed. Interpretations of the new notions in the context of reliability theory are given. Some examples illustrate the theory. This second paper introduces analogous negative dependence notions. It does this by requiring various iterated integrals of the density of a multivariate random vector to be strongly reverse regular of order 2 in the sense of \textit{S. Karlin} and \textit{Y. Rinott} [J. Multivariate Anal. 10, 499-516 (1980; Zbl 0469.60007)]. Various properties of these negative dependence notions are obtained. Some relationships with other negative dependence concepts are also given.
scientific article; zbMATH DE number 4007486