Inference for the Lognormal Mean and Quantiles Based on Samples With Left and Right Type I Censoring

Interval estimation of the mean and quantiles of a lognormal distribution is addressed based on a type I singly censored sample. A special case of interest is that of a sample containing values below a single detection limit. Generalized inferential procedures which utilize MLE based approximate pivotal quantities, and some likelihood based methods, are proposed. The latter include methodology based on the signed log-likelihood ratio test (SLRT) statistic and the modified signed log-likelihood ratio test (MSLRT) statistic. The merits of the methods are evaluated for a left censored sample using Monte Carlo simulation. For inference concerning the lognormal mean, the SLRT is to be preferred for left-tailed testing, generalized inference for right-tailed testing, and all three approaches provide nearly the same performance for two-tailed testing. These conclusions hold even when the proportion of censored values is as large as 0.70. For inference concerning quantiles, both the generalized inference approach and the MSLRT approach are satisfactory. In view of its simplicity and ease of understanding and implementation, the generalized inference procedure is to be preferred. The results are illustrated with two examples. Technical derivations are given on the Technometrics web site, as supplementary material.