Comparing some estimation methods for Frechet Distribution (Simulation)

The Frechet distribution, widely utilized in various fields such as hydrology, finance, and environmental sciences, poses challenges in parameter estimation, This study aims to compare several estimation methods for the Frechet distribution under scenarios with outlier observations. We consider both classical and robust estimation techniques, including ( Maximum Likelihood Estimation (MLE), Method of Moments (MOM), Least Squares Estimation (LSE), and Robust Regression methods(RRE)). To evaluate the performance of these methods, extensive simulation studies are conducted under different sample sizes and intial parameter values .mean squared error, are employed to assess the accuracy and robustness of each method under varying conditions. Our findings provide insights into the effectiveness and limitations of different estimation approaches for the Frechet distribution when simulation parameters are present, aiding practitioners in selecting suitable methods for robust parameter estimation in practical applications. Simulation results show that estimation method effected with (sample size, initial parameter values and evaluation criteria) , Bayesian estimation methods can be compared with Non-Bayesian estimation methods for Frechet distribution.