K. Krishnamoorthy
University of Louisiana at Lafayette

Confidence Limits for Lognormal Percentiles and for Lognormal Mean based on Samples with Multiple Detection Limits

The problem of assessing occupational exposure using the mean or an upper percentile of a lognormal distribution is addressed. Inferential methods for constructing an upper confidence limit for an upper percentile of a lognormal distribution and for finding confidence intervals for a lognormal mean based on samples with multiple detection limits are proposed. The proposed methods are based on the maximum likelihood estimates. They perform well with respect to coverage probabilities as well as power, and are satisfactory for small samples. The proposed approaches are also applicable for finding confidence limits for the percentiles of a gamma distribution. An advantage of the proposed approach is the ease of computation and implementation. An illustrative example with real data sets is given.