On a New Measure of Linear LocalDependence

Recently attempts have been made to construct some measures to compute the local dependence between two random variables. Bairamov et al. (2003) introduced a measure of local dependence which is essentially an extension of Galton correlation coefficient. In the present paper, we give an extension of the measure of local dependence, given by the cited authors, and study some of its properties. In particular, we show that our measure of local dependence can be applied to measure the dependency between two residual lifetime random variables. In this case, we give an estimator of the proposed measure of local dependency based on the bivariate mean residual lifetime. The connections between different forms of local dependency measure given in this paper and some other concepts of dependency are also investigated