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

Abstract

This study compares parameter estimation methods for the unit inverseWeibull distribution under ranked set sampling (RSS) and simple randomsampling (SRS). We examine Maximum Product Spacing Estimation, Ordi-nary Least Squares Estimation, Maximum Likelihood Estimation, WeightedLeast Squares Estimation, Anderson-Darling Estimation, Left-Tail Anderson-Darling Estimation, Right-Tail Anderson-Darling Estimation, Cram´er-vonMises Estimation, Minimum Spacing Absolute Distance Estimation, Mini-mum Spacing Square Distance Estimation, Minimum Spacing Absolute-LogDistance Estimation, and Minimum Spacing Square Log Distance Estima-tion. Monte Carlo simulations evaluate estimator performance using meansquared error, bias, and mean absolute relative error. A COVID-19 datasetvalidates the practical applicability of the methods. Results show RSS-basedestimators consistently outperform SRS counterparts across all metrics andestimation techniques. RSS demonstrates superior accuracy with reducedbias and lower mean squared error, particularly in small sample scenar-ios. These findings establish RSS as the preferred approach for unit inverseWeibull parameter estimation, providing significant improvements in statis-tical efficiency and reliability for practical applications