Estimators for type-II censored (log)normal samples

Three common estimators for the parameters of the log-normal distribution are evaluated for censored samples. Correction factors which eliminate essentially all the bias, and formulas for the standard deviations of the estimators, are presented. It is reported that the Persson-Rootzen estimators are about as good as the maximum-likelihood estimators, without the penalty of requiring iterative (computer) optimization. Also, the estimators resulting from (least squares) fitting a line to the plot of log lifetimes on normal (Gaussian) probability paper are reasonably good. Formulas are given for obtaining these latter estimators without actually plotting the points. The author simulated 5 k to 30 k samples (more samples for smaller N for each case) and calculated the following: the means, standard deviations, and third moments of each estimator; correlations between the two members of each pair; comparisons between the estimators; and simple corrections to improve the performance of the estimators