Abstract: This paper studies the dependence order among multivariate extreme value distributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.

Key words: copulas, multivariate extreme value, dependence order, positively dependent;
Frechet-Hoeffding upper bound