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Exact expressions for the bias and variance of estimators of the mean of a lognormal distribution.

Authors
Attfield-MD; Hewett-P
Source
Am Ind Hyg Assoc J 1992 Jul; 53(7):432-435
NIOSHTIC No.
00208666
Abstract
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.
Keywords
NIOSH-Author; Mathematical-models; Industrial-hygiene; Analytical-methods; Statistical-analysis; Statistical-quality-control;
CODEN
AIHAAP
Publication Date
19920701
Document Type
Journal Article;
Fiscal Year
1992
NTIS Accession No.
NTIS Price
Issue of Publication
7
ISSN
0002-8894
Source Name
American Industrial Hygiene Association Journal
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