On weighted least squares estimation for parameters of the two-parameter Weibull distribution

This paper presents an alternative method for calculating weights to be used in weighted least squares estimation (WLSE) technique for estimating the two Weibull parameters. As a common practice, weights are calculated by the reciprocals of the variances of predictor variable values. The existing WLSE methods including Bergman [101, Faucher and Tyson [11], Hung [12] and Lu et al. [13] use approximated values of the variances to calculate weights. In fact, the exact values of the variances of predictor variable values can be deducted through analytical analysis. The present paper describes the method for deducing the exact values of the variances, and also provides an approximation formula to simplify the calculation. Step-by-step procedures are provided for the proposed WLSE technique. Simulation results show that for estimating the shape parameter, the proposed procedure is more accurate than the existing WLSE methods and always generates smallest mean square error (MSE).