Using Stein’s loss function on Bayesian Estimation of Kumaraswamy-Weibull Distribution Shape Parameters with Application

Abstract

The subject of this research is the estimate of parameters for the Kumaraswamy–Weibull distribution byemploying Bayesian methods while taking Stein’s loss function into consideration. For assuring impartiality in inference,the Bayesian technique is established by adopting Jeffreys prior as a noninformative posterior distribution. We comparethe Bayesian estimators with traditional methods, specifically the method of moments estimation (ME) and the maximumlikelihood estimation (MLE), to evaluate the effectiveness of the previous method. The evaluation is carried out by means ofsimulation studies and applications involving real data, with the mean squared error (MSE) serving as the primary criterion ofcomparison. The Bayesian estimators under Stein’s loss function routinely outperform the conventional techniques, resultingin lower MSE values and displaying improved stability. This is demonstrated by the fact that the results consistently appearin a positive manner. These findings give further evidence that the Bayesian framework offers a tool that is both more reliableand more efficient for parameter estimation in the context of lifespan modeling and reliability applications.