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Finding maximum likelihood estimators for the three-parameter Weibull distribution |
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| Authors: | Éric Gourdin Pierre Hansen Brigitte Jaumard |
| Institution: | (1) Département de Mathématiques Appliquées, École Polytechnique de Montréal, Station  Centreville , P.O. Box 6079, H3C 3A7 Montréal, Québec, Canada;(2) Département des Méthodes Quantitatives et Systemes d'Information, GERAD and École des Hautes Études Commerciales, 5255 avenue Decelles, H3T1V6 Montréal, Québec, Canada;(3) Département de Mathématiques Appliquées, GERAD and École Polytechnique de Montréal, Station Centre-ville, P.O. Box 6079, H3C 3A7 Montréal, Québec, Canada |
| Abstract: | Much work has been devoted to the problem of finding maximum likelihood estimators for the three-parameter Weibull distribution. This problem has not been clearly recognized as a global optimization one and most methods from the literature occasionally fail to find a global optimum. We develop a global optimization algorithm which uses first order conditions and projection to reduce the problem to a univariate optimization one. Bounds on the resulting function and its first order derivative are obtained and used in a branch-and-bound scheme. Computational experience is reported. It is also shown that the solution method we propose can be extended to the case of right censored samples. |
| Keywords: | Global optimization decomposition maximum likelihood estimation Weibull distribution |
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