On Some Permissible Estimators of the Location Parameter of the Weibull and Certain Other Distributions

In this paper an estimator of the location parameter of the Weibull distribution is proposed which is independent of its scale and shape parameters. Several properties of this estimator are established which suggest a proper choice of three ordered sample observations insuring a permissible estimate of the location parameter. This result is valid for every distribution which has the location parameter acting as the origin or threshold parameter. Asymptotic properties of such an estimator of the location parameter of the Weibull distribution is discussed. Finally, the paper contains a brief discussion on a percentile estimator of the location parameter of the Weibull distribution and includes some numerical illustration.