Confidence limits for lognormal percentiles and for lognormal mean based on samples with multiple detection limits.
Krishnamoorthy K; Xu Z
Ann Occup Hyg 2011 Jun; 55(5):495-509
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 applicable to small sample sizes. The proposed approaches are also applicable for finding confidence limits for the percentiles of a gamma distribution. Computational details and a source for the computer programs are given. An advantage of the proposed approach is the ease of computation and implementation. Illustrative examples with real data sets and a simulated data set are given.
Mathematical-models; Statistical-analysis; Exposure-levels; Exposure-limits; Permissible-concentration-limits; Permissible-limits; Sampling; Analytical-processes; Analytical-models; Risk-analysis; Computer-models;
Author Keywords: exceedance probability; gamma distribution; left-censored samples; non-central t; ROS method; tolerance limits
Kalimuthu Krishnamoorthy, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508-1010, USA
Annals of Occupational Hygiene
University of Maryland, Baltimore