Reverse Exchangeability and Extreme Order Statistics

TL;DR

This paper introduces symmetry-based conditions for stochastic orderings among absolute values and extrema of bivariate and multivariate random vectors, enhancing understanding of their probabilistic relationships.

Contribution

It presents new symmetry conditions that establish stochastic orderings among absolute values and extrema for bivariate and multivariate vectors.

Findings

Symmetry conditions imply stochastic orderings among |X|, |Y|, max(X,Y), min(X,Y).

Partial extensions to multivariate vectors are provided.

Results improve understanding of extremal behavior under symmetry assumptions.

Abstract

For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also given.