Comments doncerning exact expressions for the bias and variance of estimators of the mean of a lognormal distribution.
Dewell-P; Attfield-MD; Hewett-P
Am Ind Hyg Assoc J 1993 Mar; 54(3):A-86-A-87
A letter to the editor was written concerning a recent publication dealing with the exact expressions for the bias and variance of estimators of the mean of a lognormal distribution. The letter critisized the authors of the original work for suggesting that the computation of the minimum variance unbiased (MVU) estimator of the arithmetic mean and arithmetic variance of data, which are log normally distributed, is both difficult and tedious. The letter stated that while the equations provided may appear to be formidable, they can be evaluated quickly to any desired degree of accuracy in only a few lines of a BASIC program or on a programmable pocket calculator. The letter provided a listing using the recurrence formula for the power series to calculate the MVU estimates of the arithmetic mean and variance of lognormally distributed data. The authors of the original article responded to the letter by suggesting that they did not mean to indicate that the estimation by the summation of a series may be a deterrent to its use. They also understood that the availability of personal computers makes such calculations far more readily completed.
NIOSH-Author; Air-quality-monitoring; Air-sampling; Computers; Mathematical-models; Statistical-analysis; Computer-models; Industrial-hygiene
American Industrial Hygiene Association Journal