On an Alternative Method of Estimation for Weibull Distribution

Abstract

In this study, the parameters of the limiting maximum Weibull distribution were estimated using a Combined Estimation Method (CEM) that combines the robustness of Trimmed L-moments (TL-moments (1,0)) with the efficiency of Maximum Likelihood Estimation (MLE). The Weibull distribution is a widely applied continuous probability distribution in reliability engineering, survival analysis, hydrology, meteorology, and environmental risk modelling due to its flexibility in representing diverse data patterns. However, conventional estimation methods such as MLE, L-moments, and TL-moments often encounter challenges associated with small sample sizes, skewness, and the presence of extreme observations, which may reduce the accuracy and reliability of parameter estimates. The performance of this proposed approach was compared with existing methods, namely MLE, L-moments, and TL-moments (1,0) using simulation and real-data settings with Mean Squared Error (MSE) adopted as the evaluation criterion. The analysis was carried out using Monthly Maximum Temperature (°C) data obtained from the Nigerian Meteorological Agency (NiMet), Lagos State, covering the period 2020 to 2024. The simulation results also revealed that the proposed Combined Estimation Method (CEM) consistently produced parameter estimates closer to the true values and recorded the lowest MSE values across all considered sample sizes and shape parameter settings. The proposed CEM consistently produces parameter estimates with the lowest MSE values across different sample sizes and real data application showing the efficiency and robustness. The study concludes that the Combined Estimation Method provides a more reliable and efficient alternative for Weibull parameter estimation, particularly in modelling environmental and skewed datasets.