Local Dependence Measures, Properties and Applications

Dependence relation between random variables is one of the most widely studied topics in probability theory and statistics. Unless specific assumptions are made about the dependence, no meaningful statistical model can be constructed. Dependence structure between random variables is generally complex and the single scalar dependence measures cannot be adequate to explain the natural association between them. With this motivation, a new local dependence function characterizing dependence structure between two random variables in an epsilon-neighbourhood of particular point from the domain of underlying bivariate distribution is introduced and its properties are investigated. Examples for the local dependence function of some bivariate distributions are provided. Also, local numerical characteristics of random variables are introduced and their properties are investigated. Local characteristics of some distributions are also examined. The text mainly provides a detailed overview of the dependence concept.In addition to explaining the theoretical concept of dependence, it also includes practical discussions.