Some Counterexamples in Positive Dependence

Taizhong Hu, Alfred M¸ller, and Marco Scarsini: December 2002, revised March 2003 and June 2003

Abstract: 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 supermodular dependence, and supermodular dependence versus positive orthant dependence