Ranked Set Sampling-Based Statistical Inference for the Exponentiated Inverted Weibull Distribution and its Variants: Theory, Simulation and Data-Driven Analysis

Abstract

When measuring a key variable is difficult or expensive, ranked set sampling provides an effective alternative for collecting data. This study investigates the estimation of parameters for the exponentiated inverted Weibull distribution using ranked set sampling and its specific forms, including extreme ranked set sampling and median ranked set sampling. Since the exponenti-
ated inverted Weibull distribution is widely applied in the analysis of lifetime and reliability data, obtaining precise parameter estimates is essential for sound statistical inference. The research compares the maximum likelihood estimates of the distribution’s parameters under different sampling schemes, namely simple random sampling, ranked set sampling, extreme ranked set sampling, and median ranked set sampling. An extensive simulation study is conducted to assess the performance
of these estimation methods in terms of bias, mean squared error, and relative efficiency under a range of sampling conditions. The study shows that variations in the size of the set and sampling cycles influence the accuracy of the estimate, with ranked set sampling, especially its extreme and median forms, generally outperforming simple random sampling.