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.

翻译：局部相依函数在概率论与统计学的众多应用中具有重要意义。本文将Bairamov与Kotz（2000）提出并由Bairamov等人（2003）进一步发展的二元局部相依函数，扩展至三元及多元情形，用以刻画三个及以上随机变量在给定特定点处的相依性。文中探讨了三元局部相依函数的定义与性质，并以三元正态分布为例展示了其三元局部相依函数的具体形式，同时提供了相应的数值图表。此外，本文还讨论了可表征多个随机变量在特定点处相依性的多元局部相依函数的扩展形式。