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Exact expressions for the bias and variance of estimators of the mean of a lognormal distribution.
Attfield MD; Hewett P
Am Ind Hyg Assoc J 1992 Jul; 53(7):432-435
The various estimators that can be used for determining the bias and variance of the arithmetic and maximum likelihood estimators of the first moment of a lognormal distribution were discussed. Equations were given which provide exact formulas for the computation of bias and variability. Some published misconceptions and errors were also corrected with these equations. If the data are truly drawn from a lognormal distribution, these equations reaffirm that the correct maximum likelihood estimator is the estimator of choice. The results obtained with these equations should assist industrial hygienists and others in understanding the nature of maximum likelihood estimators for the lognormal. This would allow industrial hygiene studies and surveys to be better designed. Expressions for the bias and variance of the approximate maximum likelihood estimator were provided in an appendix.
NIOSH-Author; Mathematical-models; Industrial-hygiene; Analytical-methods; Statistical-analysis; Statistical-quality-control;
Issue of Publication
American Industrial Hygiene Association Journal
Page last reviewed: September 22, 2020
Content source: National Institute for Occupational Safety and Health Education and Information Division