Interface between the Ratio β with Area Under the ROC Curve and Kullback-Leibler Divergence Under the Combination of Half Normal and Rayleigh Distributions

Classifying objects/individuals is common problem of interest. Receiver Operating Characteristic (ROC) curve is one such tool which helps in classifying the objects/individuals into one of the two known groups or populations. The present work focuses on proposing a Hybrid version of the ROC model. Usually the test scores of the two populations namely normal and abnormal tend to follow some particular distribution, here in this study it is considered that the test scores of normal follow Half Normal and abnormal follow Rayleigh distributions respectively. The characteristics of the proposed ROC model along with measures such as AUC and KLD are derived and demonstrated using a real data set and simulation data sets.