Modified Moment Estimation for the Three-Parameter Weibull Distribution

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Abstract
A modification of moment estimators, in which the third moment is replaced with the first order statistic, is presented for parameters of the three-parameter Weibull distribution. Calculations are made easy with the aid of accompanying charts and tables. The modified estimators enjoy advantages over the traditional moment and maximum likelihood estimators with respect to bias and variance. Unlike the maximum likelihood estimators which break down for some values of the shape parameter, estimators presented in this paper are applicable over the entire parameter space. Two illustrative examples are included.