On a Bivariate Copula for Modeling Negative Dependence: Application to New York Air Quality Data

TL;DR

This paper introduces a new bivariate copula designed to model negative dependence between two variables, with applications demonstrated on New York City air quality data, offering a flexible tool for environmental and other sciences.

Contribution

A novel bivariate copula for negative dependence with simple dependence measures and ordering properties, applicable to real-world environmental data.

Findings

Copula captures a wide range of negative dependence.

Spearman's rho and Kendall's tau have simple one-parameter forms.

Application to NYC air quality data demonstrates practical utility.

Abstract

In many practical scenarios, including finance, environmental sciences, system reliability, etc., it is often of interest to study the various notion of negative dependence among the observed variables. A new bivariate copula is proposed for modeling negative dependence between two random variables that complies with most of the popular notions of negative dependence reported in the literature. Specifically, the Spearman's rho and the Kendall's tau for the proposed copula have a simple one-parameter form with negative values in the full range. Some important ordering properties comparing the strength of negative dependence with respect to the parameter involved are considered. Simple examples of the corresponding bivariate distributions with popular marginals are presented. Application of the proposed copula is illustrated using a real data set on air quality in the New York City, USA.