A Simulation Study of Estimators for the 2-Parameter Weibull Distribution

Abstract

Seven estimators for the scale (δ) and shape (ß) parameters and percentiles of the Weibull distribution were compared by Monte Carlo methods. The evaluated estimators include the maximum likelihood estimator (MLE), linear estimators, least squares estimators, and a moment estimator. The performance of these estimators with respect to mean square error was studied in complete and Type II censored samples of sizes 10 and 25. No estimator outperformed all the others in all situations. One estimator, however, consistently performed worse than one of the others. The following summarizes the results. 1. The MLEs performed very well in the simulation study for all parameters when estimating from complete samples of size 25. For smaller samples and/or censored samples, they still performed very well as estimators of 1/ß and the upper percentiles of the distribution. 2. The best linear unbiased estimator (BLUE) was generally better than the best linear invariant estimator (BLIE) for estimating ß and the 10-th percentile. The BLIE was generally better than the BLUE for estimating 1/ß, δ, and the 90-th percentile. The overall performance of both of these linear estimators was similar to that of the MLEs. A choice between the linear estimators and the MLEs for a specific application can be based on such considerations as the availability of tables and ease of computation. No overriding superiority of the linear estimators over the maximum likelihood estimator was demonstrated, and vice versa. 3.