Estimation on Common Shape Parameter of Two Weibull Populations with Unknown and Different Scales

Abstract

The present paper addresses the problem of point estimation of the common shape parameter of two Weibull populations with different and unknown scales. Here we take the most frequently used method, the maximum likelihood estimators (MLEs). As the closed-form for our proposed model does not exist, we compute it numerically. Certain Bayes estimators using informative prior have been obtained. Like the MLEs, the closed form of these Bayes estimators do not exist, so approximation methods proposed by Lindley, Tierney & Kadane, and the Markov chain Monte Carlo (MCMC) have been used to approximate the Bayes estimators. A detailed simulation study has been carried out to compare the performances of all the proposed estimators in terms of bias and mean squared error (MSE). From our study, we found that the MCMC approximation performs better, followed by the Tierney & Kadane approximation, the MLE and the Lindley approximation. A real-life data set is considered and analyzed for the purpose of illustration.