Efficient Estimation via Record Ranked Set Sampling for Copula-Linked Bivariate Exponentiated Inverted Weibull Distributions

Abstract

 This research examines the parameter estimation in the Morgenstern-type bivariate exponentiated inverted Weibull distribution (MTBEIWD) utilizing an innovative sampling framework grounded in concomitant record ranked set sampling (CRRSS). The main aim is to obtain the best linear unbiased estimate (BLUE) for the population mean using the CRRSS method and to assess its efficacy relative to the estimate derived using concomitant record values (CRV). Explicit formulations for the BLUE, its variance, and associated coefficients are derived using both methodologies. A thorough simulation study is performed to evaluate the influence of correlation between auxiliary and primary variables, along with the effect of sample size. The findings indicate that the CRRSS-based BLUE constantly surpasses the CRV-based estimate in efficiency, especially under elevated correlations and bigger sample sizes. Graphical evaluations corroborate these findings, demonstrating enhanced stability and accuracy in the estimations derived by CRRSS. This study emphasizes the practical benefits of integrating auxiliary information and record-based sampling into the estimate process, providing a more efficient method for parameter inference in bivariate reliability and lifetime models.