Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 Articles in Press 2025 02 11 Unified estimation of $P(X>Y)$ in the generalized scale-exponential family distributions 5675 10.22060/ajmc.2025.23864.1314 EN Samira Nasr Esfahani Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran 0000-0002-1725-5937 Adel Mohammadpour Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran 0000-0002-5079-7025 Journal Article 2025 01 28 This article presents a unified approach for estimating $P(X>Y)$, also known as the area under the receiver operating characteristic (ROC) curve (AUC) or stress–strength model in the generalized scale-exponential family of distributions. The proposed framework includes the derivation of the maximum likelihood estimator and the construction of both asymptotic and percentile boot confidence intervals.