Minimum-Distance Estimation of the Parameters of the 3-Parameter Weibull Distribution

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Abstract
A 3-phase estimation technique is developed and applied to the 3-parameter Weibull distribution using location improvement through minimum-distance estimation techniques. A Monte Carlo analysis was conducted on five members on the Weibull distribution (shape parameter 0.5, 1(1)4) with sample sizes of 4(4)20. Each sample size was drawn 1000 times from each of the distributions. Three new estimators were developed. All the new estimators were compared with maximum likelihood estimators. The criteria for comparison was the ratio of the mean square errors of the parameter estimates. All of the new estimators provided better estimates than the maximum likelihood estimators. The technique using the Anderson Darling statistic provided the best overall estimates of the parameters.