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The Receiver Operating Characteristic (ROC) Curve is used to assess a biomarker's ability to discriminate between nondiseased and diseased subjects. This paper studies the parametric ROC curve assuming a Constant Shape Bi-Weibull distribution to the biomarker values, called the Constant Shape Bi-Weibull ROC (WROC) model. The research focuses on how the biomarker distinguishes between diseased and nondiseased subjects using the parametric WROC curve. The properties of the WROC curve are discussed using the concept of Kullback-Leibler Divergence (KLD) to study symmetric and asymmetric properties. The KLD is estimated using a simulation study and a real data set. The paper also discusses the accuracy of diagnostic tests, which depends on two populations and their characteristics. The ROC curve is a graphical representation of the relationship between sensitivity and specificity, and its accuracy is typically evaluated by sensitivity and specificity. The area under the ROC curve (AUC) describes the ability of the test to discriminate between diseased and nondiseased populations.