  Based on recent progress in research on copula based dependence measures, we
review the original Renyi's axioms on symmetric measures and propose a new set
of axioms that applies to nonsymmetric measures. We show that nonsymmetric
measures can actually better characterize the relationship between a pair of
random variables including both independence and complete dependence. The new
measures also satisfy the Data Processing Inequality (DPI) on the * product on
copulas, which leads to nice features including the invariance of dependence
measure under bijective transformation on one of the random variables. The
issues with symmetric measures are also clarified.
