A Note on the Relations Between Some Concepts of Positive Dependence

In this article, we provide some explicit examples showing that weak association in sequence is strictly weaker than weak association and strictly stronger than positive supermodular dependence. Furthermore, we show that strongly positive orthant dependence is strictly weaker than weakly association and strictly stronger than positive orthant dependence. Finally, we also show that positive supermodular dependence is not stronger than strongly positive orthant dependence.