Proceedings of the Joint Statistical Meetings
American Statistical Association
Weibull, Distribution Fitting, Least Squares
Least Squares estimation of the 2-parameter Weibull distribution is straightforward; however, there are multiple methods for least squares estimation of the 3-parameter Weibull. The third parameter for the 3-parameter Weibull distribution shifts the origin from 0 to some generally positive value sometimes called the location, threshold, or minimum life. The different methods used by the packages result in fairly major differences in the estimated parameters between the statistical packages. This may have implications for those needing to estimate or apply the results of a 3-parameter Weibull distribution that is used frequently in practice. The results are analyzed in detail based on an experimental design using pseudo-random Weibull data sets.
Harper, William V. and James, Thomas R., "Concerns about Least Squares Estimation for the Three-Parameter Weibull Distribution: Case Study of Statistical Software" (2015). Mathematics Faculty Scholarship. Paper 25.