This paper formulates a mathematical model for generating receiver operating characteristic (ROC) curves without underlying data. Credit scoring practitioners know that the Gini coefficient usually drops if it is only calculated on cases above the cutoff. This fact is not a mathematical necessity, however, as it is theoretically possible to get an ROC curve that keeps the same Gini coefficient no matter how big a share of lowest...

The AUC, i.e. the area under the receiver operating characteristic (ROC) curve, or its scaled version, the Gini coefficient, are the standard measures of the discriminatory power of credit scoring. Using binormal ROC curve models, we show how the shape of the curves affects the economic benefits of using scoring models with the same AUC. Based on the results, we propose that the shape parameter of the fitted ROC curve is reported...

In the practice of credit-risk management, the models for receiver operating characteristic (ROC) curves are helpful in describing the shape of an ROC curve, estimating the discriminatory power of a scorecard, and generating ROC curves without underlying data. The primary purpose of this study is to review the ROC curve models proposed in the literature, primarily in biostatistics, and to fit them to actual credit-scoring ROC data...

Credit scoring models constitute an inevitable element of modern risk and profitability management in retail financial lending institutions. Quality,or separation power of a credit scoring model is usually assessed with the Gini coefficient. Generally, the higher Gini coefficient the better, as in this way a bank can increase number of good customers and/or reject more bad applicants. In...

ROC curves, which derive from signal detection theory, are widely used to assess binary classifiers in various domains. The AUROC (area under the ROC curve) ratio or its transformations (the Gini coefficient) belong to the most widely used synthetic measures of the separation power of classification models, such as medical diagnostic tests or credit scoring. Frequently a need arises to model an ROC curve. In the biostatistical...