Comparing linear regression and maximum likelihood methods to estimate Weibull distributions on limited data sets: systematic and random errors

The present paper compares the bias and scatter of the Weibull shape parameter as estimated with the Maximum Likelihood method (ML) and four Linear Regression techniques (LR). For small data sets the bias and scatter can be very significant. It is found that ML and weighted LR give similar results. LR requires to select a plotting position. The effect of the plotting position is shown. Two changes may be used for the revised IEEE guide: plots with expected plotting positions and re-evaluation of ML and LR.