The Least Square and the Weighted Least Square Methods for Estimating the Weibull Distribution Parameters – A Comparative Study

Abstract

In this paper we study the performance of the least square method and the weighted least square method for estimating the Weibull distribution parameters. In engineering practice these methods are commonly used due to their simplicity. The estimates of the parameters can be calculated easily by the closed-form formula. We consider three estimators of the cumulative distribution function and the weight factor proposed by Bergman (1986). The methods are compared in terms of the root mean square error and sample size. The comparison is based on the Monte Carlo simulation. The comparison shows that the weight factor improves the accuracy of the estimation the Weibull distribution parameters.