Point and interval estimation of R = P(X > Y) for the proportional reversed hazard family based on ranked set sampling

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.