Estimation of Area under the ROC Curve Using Exponential and Weibull Distributions

In recent years the Receiver Operating Characteristic (ROC) curves received much attention in medical diagnosis for classifying the subjects into one of the two groups. Many researchers have provided the mathematical formulation of the curve by assuming some specific distribution. Conventionally, much work has been carried out by assuming normal distribution. In this paper, we focused on estimating the ROC Curve and Area Under the Curve (AUC) using Exponential and Weibull distributions. As Exponential and Weibull distributions are important in life testing problems, the performance of ROC forms of these distributions are studied and then results are compared with conventional Binormal ROC form. The entire study was done using real and simulated data sets. In a perspective it is proposed that ROC form of Binormal is far better than the other two and Biexponential is better than the Biweibull model of ROC curve.