Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling

Sampling methods are fundamental approaches that enhance the efficiency of scientific studies. However, to minimize ranking errors and obtain more accurate estimators, it is essential to develop alternative techniques to classical methods. The Median Ranked Set Sampling (MRSS) method stands out as a robust tool that minimizes ranking errors and enables more efficient evaluation of data. This method is particularly effective in improving the accuracy of sampling processes. On the other hand, the Unit-Gompertz (UG) distribution, with its flexible structure and parameters confined to the [0,1] interval, has emerged as a significant modeling option in fields such as health sciences, reliability theory, and actuarial studies. This study aims to analyze the performance of the MRSS method for the unknown parameters of the UG distribution and compare it with the Simple Random Sampling (SRS) method to develop more effective estimations. In addition to simulation results, a real-data application is also provided to demonstrate the practical usefulness of the proposed approach. The results demonstrated that MRSS provides more accurate and efficient estimates compared to SRS.