We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. An END sequence has a partial sum which, subtracted by its mean, does not diverge as the number of random variables goes to infinity. We show that an END...

Following the results of Rüschendorf and Uckelmann (2002) [20], we introduce the completely mixable distributions on and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem for convex functions f...