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...

We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the...

A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are...

We settle an open conjecture regarding the newsvendor game. We prove that its core is always nonempty for all possible joint distributions of the random demands. We give sufficient conditions under which the core is a singleton, or at a core allocation every newsvendor shares a nonnegative cost