In classification, the Receiver Operating Characteristics (ROC) curve analysis is one of the most familiar techniques and it will provide accuracy for the extent of correct classification of a test. The conventional way of expressing the true accuracy of test is by using its summary measure Area Under the Curve (AUC) and intrinsic measures Sensitivity and Specificity. Brier Score (B̅) is shown as another summary measure in the context of ROC Curve to make the probabilistic judgments as well as to identify the extent of classification. Further, the Functional relationship between the Brier Score and AUC of ROC Curve is provided using the parameters b (ratio of standard deviations of signal and noise) and α (priori probability).The influence of slope on ROC curve is highlighted to explain the behavior of Brier Curves and its relationship with AUC. To demonstrate the proposed methodology Simulation Study is conducted at different combinations of scale parameters of both populations. If parameters b and α are constants, B̅ values in relation to given AUC values if B̅ values monotonically decreases as AUC values increases, and these relationship curves have monotonically decreasing slopes. An illustrative example is also provided to explain the concepts
