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.
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Gourdin, É., Hansen, P. & Jaumard, B. Finding maximum likelihood estimators for the three-parameter Weibull distribution. J Glob Optim 5, 373–397 (1994). https://doi.org/10.1007/BF01096687
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DOI: https://doi.org/10.1007/BF01096687