A data driven parameter estimation for the three parameter Weibull population from censored samples

Abstract

A method is described for the calculation of the three-parameter Weibull distribution function from censored samples. The method introduces a data driven technique based on an adapted Gaussian like kernel to match the censoring scheme. The method minimizes the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likelihood estimators are found and a comparison is made with the new estimator. A Monte Carlo experiment of size 1000 is conducted to test the performance of the new parameter estimation technique. The mean integrated square error is taken as a measure of the closeness of the estimated density and the true density.