Small-Sample Estimation for the Lognormal Distribution With Unit Shape Parameter

Let X be a random variable such that In [(X - ¿)/¿] has a s-normal distribution with mean zero and variance one. Then X has a 3-parameter lognormal distribution with the third parameter, the shape parameter, fixed at unity. This paper presents the coefficients required to construct the best linear unbiased estimators (BLUEs) of ¿ and ¿ for samples of size fifteen and less. The variances and covariances of these estimators are provided. These estimators yield the BLUEs of the mean, standard deviation, and percentiles of X since these quantities are linear functions of ¿ and ¿. Blom´s estimators and maximum likelihood estimators compare favorably with the BLUEs.