A receiver operating characteristic (ROC) curve shows the performance of a binary classification model as its discrimination threshold varies. For a range of thresholds, the curve plots the true positive rate against the false positive rate.
The true positive rate (also called sensitivity or recall) measures the percentage of positive observations that are correctly classified (for example, the percentage of sick people who are correctly identified as having the disease).
The false positive rate is the percentage of negative observations that are incorrectly classified (for example, the percentage of healthy people who are incorrectly identified as having the disease).
The area under the ROC curve (AUC or AUROC) is a measure of the quality of a particular classifier. A random classifier (shown as a straight line in the preceding figure) has an AUC of 0.5. A perfect classifier has an AUC of 1.0.
The Gini coefficient is a measure of inequality among values of a frequency distribution. A Gini coefficient of 0 indicates that all values are the same. The closer the Gini coefficient is to 1, the more unequal are the values in the distribution.
This formula calculates the Gini coefficient, G, from the AUC: G = 2*AUC-1