A consistent method of estimation for the three-parameter lognormal distribution based on Type-II right censored data

In 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.