On estimating Weibull modulus by the linear regression method

Statistical models were developed to estimate the bias of the shape parameter of a 2-parameter Weibull distribution where the shape parameter was estimated using a linear regression. These models were formulated for 27 sample sizes from 5 to 100 and for 35 probability estimators, \( P = {(i - a)} \mathord{\left/ {\vphantom {{i - a} {n + b}}} \right. \kern-\nulldelimiterspace} {(n + b)} \), by varying “a” and “b”. In each simulation, 20,000 trials were used. From these models, a class of unbiased estimators were developed for each sample size. The standard deviation and coefficient of variation of these estimators were compared to the bias of the estimators. The standard deviation increased while the coefficient of variation decreased with increasing bias of the shape parameter. Also, the Anderson–Darling statistics was used to determine that the normal, log-normal, 3-parameter Weibull, and 3-parameter log-Weibull distributions did not provide good fit to the estimator of the shape parameter.