In this article, we examine the point and interval estimation of \(R=P(X>Y)\) under the simple random sampling (SRS), ranked set sampling (RSS), and median ranked set sampling (MRSS) plans when the X and Y random variables follow the distributions from the proportional reversed hazard (PRH) family. In the framework of point estimation, we obtain the estimate of R by using the maximum likelihood method. Also, in the cases of RSS and MRSS plans, we use a modified maximum likelihood method to determine the closed form of R. In the framework of interval estimation, we create the asymptotic confidence interval of R based on all three sampling methods. In addition, the exact confidence interval is constructed by employing the pivotal quantity technique based on the SRS plan. A study is performed using a simulation technique to compare the suggested methods. The results are obtained under the Topp–Leone distribution as an example of the PRH family. Finally, frosted flakes data is used to explain the application of the studied methods.
