Mathematics Faculty Scholarship

Document Type

Conference Proceeding

Publication Date


Publication Title

JSM Proceedings, Risk Analysis Section


American Statistical Association


Weibull, Maximum Likelihood, Reliability


Maximum Likelihood estimation of the two-parameter Weibull distribution is straightforward; however, there are multiple methods for maximum likelihood estimation of the three-parameter Weibull. This paper presents an evaluation of these methods using four data sets including oil spill data from the Gulf of Mexico. Highlighted are fairly major differences in the estimated parameters between nine statistical packages. A VBA routine has been developed allowing practitioners to implement three-parameter Weibull maximum likelihood estimate within Excel. The code and support documentation are available free at

First Page


Last Page



Authors retain copyright on individual papers published in the JSM Proceedings.

Original Citation

Harper, William V., Thomas R. James, Ted G. Eschenbach, Leigh Slauson (2008), "Maximum Likelihood Estimation Methodology Comparison for the Three-Parameter Weibull Distribution with Applications to Offshore Oil Spills in the Gulf of Mexico", JSM Proceedings, Risk Analysis Section, pp. 1231-1238, American Statistical Association, Denver, CO.


Publisher's Version

Peer Reviewed




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