Comparison of means of two lognormal distributions based on samples with multiple detection limits.

The problem of comparing the means of two lognormal distributions based on samples with multiple detection limits is considered. Tests and confidence intervals for the ratio of the two means, based on pivotal quantities involving the maximum likelihood estimators, are proposed. The merits of the proposed approaches are evaluated by Monte Carlo simulation. Simulation study indicates that the procedures are satisfactory in terms of coverage probabilities of confidence intervals, and powers of tests. The proposed approach can also be applied to find confidence intervals for the difference between the means of the two lognormal distributions. Illustrative examples with a real data set and with a simulated data set are given.