Directional Dependence Orders of Random Vectors

Abstract

In this paper, we define a multivariate order based on the concept of orthant directional dependence and study some of its properties. The relationships with other dependence orders given in the literature are also studied. We analyze the order between two random vectors in terms of their associated copulas and illustrate our results with several examples.

Monotonic Random Variables According to a Direction

“…These comparative analyses shed light on the interconnectedness and compatibility between different analytical approaches, enriching our understanding of multivariate dependence. The exploration of I(α) stochastic orders-closely resembling those studied in [21]-is ongoing and represents a fertile ground for future research.…”