Unified estimation of $P(X>Y)$ in the generalized scale-exponential family distributions

Nasr Esfahani, Samira; Mohammadpour, Adel

doi:10.22060/ajmc.2025.23864.1314

Unified estimation of $P (X > Y)$ in the generalized scale-exponential family distributions

Articles in Press

Document Type : Original Article

Authors

Samira Nasr Esfahani
Adel Mohammadpour

Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

10.22060/ajmc.2025.23864.1314

Abstract

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.

Keywords