Characterizations Using Local Dependence Function

Abstract

In this article, we study the properties of the local dependence function, introduced by Holland and Wang [Holland, P. W., Wang, Y. J. (1987). Dependence function for continuous bivariate densities. Commun. Statist. Theory and Methods 16:863–876] in the context of reliability modeling. It is shown that one component of the vector failure with the local dependence function determines the joint bivariate density uniquely. Furthermore, we present characterizations for bivariate Lomax distribution, bivariate Dirichlet distribution, and bivariate normal distribution using local dependence function and regression functions.