The multivariate local dependence function

TL;DR

This paper extends the concept of local dependence functions from bivariate to multivariate cases, providing definitions, properties, and examples for three or more variables to better characterize their dependencies at specific points.

Contribution

It introduces a multivariate local dependence function, generalizing previous bivariate models, with detailed properties and an example for the multivariate normal distribution.

Findings

Defined the three-variate local dependence function

Provided properties and theoretical discussion

Presented an example with multivariate normal distribution

Abstract

The local dependence function is important in many applications of probability and statistics. We extend the bivariate local dependence function introduced by Bairamov and Kotz (2000) and further developed by Bairamov et al. (2003) to three-variate and multivariate local dependence function characterizing the dependency between three and more random variables in a given specific point. The definition and properties of the three-variate local dependence function are discussed. An example of a three-variate local dependence function for underlying three-variate normal distribution is presented. The graphs and tables with numerical values are provided. The multivariate extension of the local dependence function that can characterize the dependency between multiple random variables at a specific point is also discussed.