Concerns about Least Squares Estimation for the Three-Parameter Weibull Distribution: Case Study of Statistical Software

Authors

William V. Harper, Otterbein UniversityFollow
Thomas R. James, Otterbein UniversityFollow

Document Type

Conference Proceeding

Publication Date

8-10-2015

Publication Title

Proceedings of the Joint Statistical Meetings

Publisher

American Statistical Association

Keywords

Weibull, Distribution Fitting, Least Squares

Abstract

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.

First Page

1268

Last Page

1282

Comments

Section on Physical and Engineering Sciences

Repository Citation

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. 25.
https://digitalcommons.otterbein.edu/math_fac/25

Version

Publisher's Version