Inferring association from reliability functions: An approach based on copulas

Nair, Sankaran and John (Metron 76 (2018) 133–153) have defined and studied the properties of reliability functions in terms of copulas. In the present paper, we investigate the utility of such functions in inferring the time-dependent association of bivariate distributions. We consider the Clayton measure of association for the study. A general expression for this measure in terms of the generator of Archimedean copulas is given, and a method of finding nature of association using the generators is provided. We derive the relationship of the association measure with the ageing property of the distribution, associated with the generator. We analyze how the hazard rate of survival copulas can be utilized in studying the association between two random variables. Applications of the results in real life situations are discussed.