Statistical Inference for the Unit Inverse Weibull Distribution Using Ranked Set Sampling with COVID-19 Application

This study compares parameter estimation methods for the unit inverse Weibull distribution under ranked set sampling (RSS) and simple random sampling (SRS). We examine Maximum Product Spacing Estimation, Ordinary Least Squares Estimation, Maximum Likelihood Estimation, Weighted Least Squares Estimation, Anderson-Darling Estimation, Left-Tail Anderson-Darling Estimation, Right-Tail Anderson-Darling Estimation, Cram´er-von Mises Estimation, Minimum Spacing Absolute Distance Estimation, Minimum Spacing Square Distance Estimation, Minimum Spacing Absolute-Log Distance Estimation, and Minimum Spacing Square Log Distance Estimation. Monte Carlo simulations evaluate estimator performance using mean squared error, bias, and mean absolute relative error. A COVID-19 dataset validates the practical applicability of the methods. Results show RSS-based estimators consistently outperform SRS counterparts across all metrics and estimation techniques. RSS demonstrates superior accuracy with reduced bias and lower mean squared error, particularly in small sample scenarios. These findings establish RSS as the preferred approach for unit inverse Weibull parameter estimation, providing significant improvements in statistical efficiency and reliability for practical applications.