Modeling directional monotonicity with copulas

TL;DR

This paper characterizes directional monotonicity of multiple random variables using copulas, extending from bivariate to multivariate cases with illustrative examples.

Contribution

It introduces a framework to understand directional monotonicity via copulas, expanding the concept from bivariate to multivariate scenarios.

Findings

Relationships established in bivariate and trivariate cases

Extension to multivariate case demonstrated

Examples provided for all studied cases

Abstract

The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and trivariate cases, which help to understand the extension to the multivariate case. Examples of copulas in all the studied cases are provided.