Equitability of Dependence Measure

A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationship of different types. In practice, we do not know what kind of functional relationship is underlying two given observations, Hence the equitability of dependence measure is critical in analysis and by scoring relationships according to an equitable measure one hopes to find important patterns of any type of further examination. In this paper, we introduce our definition of equitability of a dependence measure, which is naturally from this initial description, and Further more power-equitable(weak-equitable) is introduced which is of the most practical meaning in evaluating the equitablity of a dependence measure.