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 inverse
Weibull distribution under ranked set sampling (RSS) and simple random
sampling (SRS). We examine Maximum Product Spacing Estimation, Ordi-
nary 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, Mini-
mum Spacing Square Distance Estimation, Minimum Spacing Absolute-Log
Distance Estimation, and Minimum Spacing Square Log Distance Estima-
tion. 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 scenar-
ios. These findings establish RSS as the preferred approach for unit inverse
Weibull parameter estimation, providing significant improvements in statis-
tical efficiency and reliability for practical applications.