The Relationship between Gini Methodology and the ROC curve

Abstract

The connection between the area under the ROC curve (AUC), which is frequently used in the diagnosis and classification literature, and the Gini terminology, which is mainly used in the economic literature, is clarified. It is shown that AUC is related to the covariance between Yi, the number of 1's until the ith 0, and F(Ti), the empirical rank of the ith 0, ordered by the predictive probability.