A consistent method of estimation for the three-parameter lognormal distribution based on Type-II right censored data |
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| Authors: | Hideki Nagatsuka N. Balakrishnan |
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| Affiliation: | 1. Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japanhideki@indsys.chuo-u.ac.jp;3. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada;4. Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia |
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| Abstract: | ABSTRACTIn this paper, we propose a parameter estimation method for the three-parameter lognormal distribution based on Type-II right censored data. 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 very well compared to a prominent method of estimation in terms of bias and root mean squared error (RMSE) in small-sample situations. Finally, two examples based on real data sets are presented for illustrating the proposed method. |
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| Keywords: | Bias Consistency Existence Lognormal distribution Maximum likelihood estimation Mean squared error Monte Carlo simulation Type-II censoring Uniqueness. |
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