Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non-Censored Samples


QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, vol.29, no.8, pp.1207-1219, 2013 (SCI-Expanded) identifier identifier


The two-parameter Weibull distribution is one of the most widely applied probability distributions, particularly in reliability and lifetime modelings. Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for estimating the Weibull shape parameter and an experimental study using classical regression methods to compare the results of the methods. A complete list of the parameter estimators considered in this study is as follows: ordinary least squares (OLS), weighted least squares (WLS, Bergman, F&T, Lu), non-parametric robust Theil's (Theil) and weighted Theil's (WeTheil), robust Winsorized least squares (WinLS), and M-estimators (Huber, Andrew, Tukey, Cauchy, Welsch, Hampel and Logistic). Estimator performances were compared based on bias and mean square error criteria using Monte-Carlo simulations. The simulation results demonstrated that for small, complete, and non-outlier data sets, the Bergman, F&T, and Lu estimators are more efficient than the others. When the data set contains one or two outliers in the X direction, Theil is the most efficient estimator. Copyright (c) 2012 John Wiley & Sons, Ltd.