Bayesian Estimation of the Scale Parameter of Weibull Distribution using Ranked Set Samples

Abstract

This research article is primarily focused on the investigation of Bayes estimators for the scale parameter of the Weibull distribution. Specifically, we focus on a sampling method known as Ranked Set Sample with Unequal Samples (RSSU), as introduced and studied by Bhoj (2001). Our objective is to derive Bayes estimates for the scale parameter utilizing two distinct loss functions: the squared error loss (SEL) function and the linear exponential (LINEX) loss function. We consider the scenario where the scale parameter follows either a gamma prior distribution or a Jeffreys prior distribution. To evaluate the performance of these estimators, we conduct simulations and analyse their bias and mean squared error (MSE). Our findings show that RSSU-based estimators outperform those based on Simple Random Sampling (SRS) and Ranked Set Sampling (RSS), when either Jeffreys prior or gamma prior distribution is used.