Comparison of Means of Two Lognormal Distributions Based on Samples with Multiple Detection Limits

Abstract

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.

Keywords:

• confidence interval
• coverage probability
• difference of means
• maximum likelihood estimator
• power
• ratio 'of means
• Type I error

ACKNOWLEDGMENTS

The authors thank Professor Gurumurthy Ramachandran for reviewing the manuscript and for several helpful comments. They are also grateful to Dr. Paul Hewett for suggesting Example 2, and to two reviewers for providing detailed comments and suggestions. The work was supported by grant R01OH003628 from the National Institute of Occupational Safety and Health (NIOSH).