@article{Kotb2025, 
author = {Mohammed S. Kotb and Ghaithah A. Alzhrani},
title = {Inference of    P      (          X      <      Y        )   for two-parameter exponential-Rayleigh distribution with applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {16526-16550},
keywords = {asymptotic distributions, Bayesian estimation, confidence and credible intervals, maximum likelihood estimator, stress-strength model},
url = {https://www.sciopen.com/article/10.3934/math.2025740},
doi = {10.3934/math.2025740},
abstract = {Let    X and    Y follow independent exponential-Rayleigh distributions when the shape and scale parameters are different. In this paper, the maximum likelihood and the Bayes estimates of the stress-strength parameter    δ  =  P  (  X  <  Y  ) are derived. Based on the sampling technique, we use the asymptotic distribution and the Bayes estimate of    δ to construct the corresponding confidence and credible intervals. Analyses of two data sets, one simulated data and the other real-life data, are given for illustrative purposes. Finally, Monte Carlo simulations are used to compare the different methods discussed here.}
}