Estimation of a Linear Parametric Function Associated with the Lognormal Distribution

• Activity Number: 437
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jiangtao Gou* and Ajit Tamhane
• Companies: Northwestern University and Northwestern University
• Keywords: Bias ; Lognormal distribution ; Mean square error ; Minimum variance unbiased estimator

Abstract

Estimation of the mean of the lognormal distribution has received much attention in the literature beginning with the paper by Finney (1941). The problem is of significant practical importance because of the widespread use of log-transformation in practice. In this paper we consider estimation of a linear parametric function associated with the lognormal distribution of which the mean, median and moments are special cases. We generalize various estimators proposed in the literature for the mean to this linear parametric function and review them. Next we propose a new simple estimator that outperforms many of the previous estimators in terms of the mean square error (MSE) and bias. We derive asymptotic expressions for MSE and bias for all estimators to compare them. The asymptotic comparisons are validated in case of small samples through extensive simulations.