Maximum Likelihood Estimation for the Inverted Kumaraswamy Distribution Based on the Extreme Ranked Set Sampling

This study investigates the use of extreme ranked set sampling (ERSS) for parameter estimation in the Inverted Kumaraswamy (IK) distribution. The Kumaraswamy distribution has wide applications in fields such as reliability testing, environmental studies, financial analysis, and survival analysis. The paper emphasizes the efficiency advantages of ERSS, particularly in capturing extreme values, which are crucial for distributions with heavy tails or skewed data. By incorporating ERSS, this research demonstrates that more accurate and efficient parameter estimates can be obtained compared to traditional sampling methods like simple random sampling (SRS). A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, a real data set is presented for illustrative purposes. The findings suggest that ERSS outperforms SRS in terms of precision, particularly in contexts where extreme values play a significant role. This work contributes to the advancement of sampling techniques for extreme value contexts, with potential applications in various fields, including environmental research, finance, and reliability analysis.