Estimation of a parametric function associated with the lognormal distribution

Estimation of the mean of the lognormal distribution has received much attention in the literature beginning with Finney (1941 Finney, D.J. (1941). On the distribution of a variate whose logarithm is normally distributed. Supp. J. Royal Stat. Soc. 7(2):155–161.[Crossref] , [Google Scholar]). The problem is of significant practical importance because of the ubiquitous use of log-transformation. In this article, we consider the estimation of a parametric function associated with the lognormal distribution of which the mean, median, and moments are special cases. We generalize various estimators from the literature for the mean to this parametric function and propose a new simple estimator. We present the estimators in a unified framework and use this framework to derive asymptotic expressions for their biases and mean square errors (MSEs). Next, we make asymptotic and small-sample comparisons via simulations between them in terms of their MSEs. Our proposed estimator outperforms many of the previously proposed estimators. A numerical example is given to illustrate the various estimators.