AROC Curve and Optimal Threshold Hong, Chong-Sun; Lee, Hee-Jung;
In the credit evaluation study with the assumption of mixture distributions, the ROC curve is a useful method to explore the discriminatory power of default and non-default borrowers. The AROC curve is an adjusted ROC curve that can be identified with the corresponding score and is mathematically analyzed in this work. We obtain patterns of this curve by applying normal distributions. Moreover, the relationship between the AROC curve and many classification accuracy statistics are explored to find the optimal threshold. In the case of equivalent variances of two distributions, we obtain that the local minimum of the AROC curve is estimated at the optimal threshold to maximize certain classification accuracies.
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