Some counterexamples in positive dependence

A. Müller, M. SCARSINI

Journal of Statistical Planning and Inference

2004, vol. 124, n°1, pp.153-158

Départements : Economie et Sciences de la décision

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 (J. Math. Phys. 41 (2000) 1371) and Pellerey (Personal communication, 2002) concerning respectively association versus weak association, weak association versus supermodular dependence, and supermodular dependence versus positive orthant dependence