Aggregation of Random Variables Under Weak Stochastic Orders

Aggregations of random variables map several random variables to a new random variable, satisfying monotonicity and boundary conditions with respect to a stochastic order. Typically, the usual stochastic order (<=st) is adopted, since it allows compositions of usual aggregation functions and random vectors to be aggregations of random variables. However, quite strong conditions are needed in order to have the usual stochastic order between two random vectors, reducing its applicability. In this paper, we replace the usual s tochastic order by weaker orders, studying the usual aggregation functions that can still be used and properties concerning variability and positive-dependence bias.