A consistent method of estimation for the three-parameter Weibull distribution

Authors:
Hideki Nagatsuka;Toshinari Kamakura;N. Balakrishnan
Affiliations:
Faculty of System Design, Tokyo Metropolitan University, Asahigaoka 6-6, Hino-shi, Tokyo 191-0065, Japan;Department of Science and Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, Japan;Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Venue:
Computational Statistics & Data Analysis
Year:
2013

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Abstract

In this paper, we propose a new method for the estimation of parameters of the three-parameter Weibull distribution. The method is based on a data transformation, which avoids the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely in the entire parameter space, and the estimators also have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs better than some existing methods in terms of bias and root mean squared error (RMSE). Finally, two examples based on real data sets are presented to illustrate the proposed method.