Evaluating the Efficacy of MLE, LSE, and Moment-based Methods in Weibull Parameter Estimation

الملخص

In this study, three methods were compared for estimating two parameters from the Weibull distribution using random data. For the shape parameter (β), the Method of Moments (MOM) provided the lowest mean squared error (MSE), indicating that MOM estimated the shape parameter β more accurately than the other methods. For the scale parameter (δ), it was found that the Least Squares Estimation (LSE) gave the lowest mean squared error, suggesting it is the most accurate for estimating δ since the accuracy of estimation varies between the shape and scale parameters. The choice of the best method may depend on the particular importance of estimating β or δ accurately in the application. If precise estimation of β is more crucial, then the MOM would be preferable. Conversely, if δ is of greater importance, the Least Squares Estimation Method (LSE) seems more suitable. If a balance is necessary, one might consider adopting a composite approach or additional analysis to weigh the errors according to their impact on the model or the overall analysis.