193 – Contributed Poster Presentations: Section on Physical and Engineering Sciences
Maximum Likelihood and Least Squares Estimation Comparison for the Three-Parameter Weibull Distribution: Case Study of Statistical Software
William V. Harper
Otterbein University
Thomas R. James
Otterbein University
Both Maximum Likelihood and Least Squares estimation of the 2-parameter Weibull distribution are straightforward; however, there are concerns for their 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 sometimes result in fairly major differences in the estimated parameters between the statistical packages. This has been covered previously using modern statistical software separately for maximum likelihood and least squares (maximum likelihood, 2011: Harper, James, Eschenbach; least squares 2015: Harper, James). This publication directly compares the maximum likelihood and least squares results. The findings 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 based on an experimental design using pseudo-random Weibull data sets.