We provide some counterexamples showing that some concepts of positive dependence are strictly stronger than others. In particular we will settle two questions posed by Pemantle (2000) and Pellerey (2002) concerning respectively association versus weak association, weak association versus...

In the first part of the paper we consider positive dependence properties of Archimedean copulae. Especially we characterize the Archimedean copulae that are multivariate totally positive of order 2 (MTP2) and conditionally increasing in sequence. In the second part we investigate conditions for...