Abstract

This study aims to compare the performance of five different methods for estimating the parameters of the Frechet distribution: Maximum Likelihood Estimation (MLE), Method of Moments Estimation (MME), Least Squares Estimation (LSE), Percentile Estimation (PE), and Moments-L Estimation (ME-L). The Frechet distribution is widely used in modeling extreme data, such as floods, financial risks, and engineering failures, making accurate parameter estimation crucial for reliable statistical analysis. However, the lack of a clear standard for selecting the most efficient estimation method, especially under varying sample sizes, poses a significant challenge. To address this issue, Monte Carlo simulation was employed to evaluate the performance of these methods across different sample sizes (small, medium, and large). The evaluation was based on statistical criteria such as Mean Squared Error (MSE) and Total Deviation (TD). The results revealed that the Maximum Likelihood Estimation (MLE) method consistently provided the most accurate estimates, particularly for large samples, achieving the lowest MSE and TD values. The Moments-L Estimation (ME-L) method also demonstrated strong performance, especially in medium and large samples, offering a viable alternative with lower computational complexity. In contrast, the Method of Moments (MME) showed higher variability and less accuracy, particularly in small samples. The study highlights the importance of selecting the appropriate estimation method based on sample size and computational requirements. For large datasets, MLE is recommended due to its superior accuracy, while ME-L can be a practical alternative for medium-sized samples. The findings also suggest that further research should explore the development of more efficient algorithms for less accurate methods like MME and PE. In conclusion, this research provides valuable insights into the performance of various parameter estimation methods for the Frechet distribution, offering practical recommendations for researchers and practitioners in fields such as hydrology, engineering, and economics, where accurate modeling of data is essential. The study underscores the effectiveness of Monte Carlo simulation in evaluating statistical methods and suggests future directions for improving estimation techniques.