The multivariate local dependence function

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.