Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution

The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction of the best choice of percentiles for the method of quantiles and the joint asymptotic efficiency comparison of applied methods.