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For credit evaluation models, we extend the study of discriminatory power based on AUC obtained from a ROC curve when the number of defaults is small and distribution functions of the defaults and non-defaults are normal distributions. Since distribution functions do not satisfy normality in real world, the distribution functions of the defaults and non-defaults are assumed as normal mixture distributions based on results that the normal mixture could be better fitted than other distribution estimation methods for non-normal data. By using several AUC statistics, the discriminatory power under such a circumstance is explored and compared with those of normal distributions.

Estimating Discriminatory Power with Non-normality and a Small Number of Defaults