Procedures for estimation of Weibull parameters

Abstract

The primary purpose of this publication is to provide an overview of the information in the statistical literature on the different methods developed for fitting a Weibull distribution to an uncensored set of data and on any comparisons between methods that have been studied in the statistics literature. This should help the person using a Weibull distribution to represent a data set realize some advantages and disadvantages of some basic methods. It should also help both in evaluating other studies using different methods of Weibull parameter estimation and in discussions on American Society for Testing and Materials Standard D5457, which appears to allow a choice for the method to estimate the parameters of a Weibull distribution from a data set. Because in D5457 the method to estimate parameters is to some extent optional, the resulting fitted distribution used to derive the reference resistance properties of wood-based materials and structural connections might result in different values developed under the standard. The maximum-likelihood method appears to be the method that should be used as the default, with other methods requiring some type of justification for their use in wood utilization research.

Citation

Evans, James W.; Kretschmann, David E.; Green, David W. 2019. Procedures for estimation of Weibull parameters. Gen. Tech. Rep. FPL–GTR–264. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 17 p.