Maximum likelihood estimation for the parameters in the three-parameter Weibull distribution needs an initial value in the iteration scheme for likelihood equations. In certain cases, maximum likelihood estimation can break down for the three-parameter Weibull model, as no local maximum of the likelihood exists. To avoid these difficulties, we suggest a modification of the weighted least-squares estimators for the three-parameter Weibull distribution. The modification presented here is to find an estimate for a threshold parameter for this distribution. © 1994.
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