Equivalence between the Area under the Kolmogorov-Smirnov Curve and the Gini Index in the Performance Evaluation of Binary Decisions

• Paulo J. L. Adeodato Federal University of Pernambuco
• Sílvio B. Melo Federal University of Pernambuco

DOI: https://doi.org/10.5753/sbbd.2016.24321

Abstract

This paper proposes and proves the important equivalence between the Gini index and the area under the Kolmogorov-Smirnov (KS) distribution curve. The proof’s rationale is similar to that used in the proof of equivalence between AUC_ROC and AUC_KS. But different from that, this one uses a transformation that preserves the 1-to-1 correspondence between the ideal classifier on the KS and Lorenz curve domains. As metrics, this paper proves that the Gini index ratio to that of the ideal classifier is equivalent to the area under the KS curve ratio to that of its ideal classifier. That is Gini_Index_Ratio = AUC_KS_Ratio. This complements the proven equivalence between KS and ROC area metrics extending it to the Gini index.

Keywords: Gini Index, Kolmogorov-Smirnov, Equivalence between metrics

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