  Measuring dependence between two random variables is very important, and
critical in many applied areas such as variable selection, brain network
analysis. However, we do not know what kind of functional relationship is
between two covariates, which requires the dependence measure to be equitable.
That is, it gives similar scores to equally noisy relationship of different
types. In fact, the dependence score is a continuous random variable taking
values in $[0,1]$, thus it is theoretically impossible to give similar scores.
In this paper, we introduce a new definition of equitability of a dependence
measure, i.e, power-equitable (weak-equitable) and show by simulation that HHG
and Copula Dependence Coefficient (CDC) are weak-equitable.
