In biomedical studies bio-markers are used to distinguish between two groups of subjects usually, diseased (high risk) and non-diseased (low risk) subjects. Many diagnostic biomarkers results are continuous measurements. Some example include, serum antigen or enzyme concentrations (Zweig and Campbell 1993) are continuous in nature. The Receiver Operating Characteristic (ROC) curves have been widely used for evaluating the accuracy and discriminating power of a biomarker or statistical model. In this regard Generalized-Exponential Distribution model is suggested for analyzing such data. The model can be applied in the situations when the other well-known parametric models (e.g. the bi-normal one) cannot be used. In this paper the parametric equation of the Receiving Operating Characteristic (ROC) curve model is established under the assumptions of bi-distributional population based on pair of Generalized-Exponential Distributions. Also its maximum likelihood estimator MLE, sampling distribution, equivalence test statistic and exact confidence interval are derived.