Median Based Unit Weibull Distribution (MBUW): Do the Higher Order Probability Weighted Moments (PWM) Add More Information over the Lower Order PWM in Parameter Estimation

Abstract

This paper offers an in-depth investigation into the Probability Weighted Moments (PWMs) methodology for estimating parameters of the Median Based Unit Weibull (MBUW) distribution. The author delves into a thorough comparison of the commonly employed first-order PWMs against more advanced higher-order PWMs. The analysis highlights the significant benefits associated with adopting these more sophisticated techniques, particularly in terms of accuracy and reliability in parameter estimation. In addition to this comparative analysis, the author derives the asymptotic distribution of the PWM estimator, which provides a theoretical foundation for the results and enhances the robustness of the conclusions. To further illustrate the practical implications of the findings, the author includes a detailed real data analysis that exemplifies the effectiveness of the proposed methodology. Through these examples, the author underscores the relevance of PWMs in real-world applications, demonstrating how this approach can lead to improved parameter estimates when working with the MBUW distribution.