In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate...

In this paper, we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing the previous upper and lower orthant orders. The main properties of this new order, together with its relationships with other...

We propose a new multivariate order based on a concept that we will call extremality". Given a unit vector, the extremality allows to measure the "farness" of a point with respect to a data cloud or to a distribution in the vector direction. We establish the most relevant properties of this...