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Journal of Probability and Statistics
Volume 2014 (2014), Article ID 964197, 7 pages
http://dx.doi.org/10.1155/2014/964197
Research Article

Increased Statistical Efficiency in a Lognormal Mean Model

1College of Pharmacy & Peggy and Charles Stephenson Cancer Center, The University of Oklahoma Health Sciences Center, 1110 North Stonewall Avenue, Oklahoma City, OK 73126-0901, USA
2Department of Mathematics & Statistics, Faculty of Science and Technology, The University of the West Indies, St. Augustine Campus, Debe, Trinidad and Tobago

Received 14 October 2013; Revised 27 February 2014; Accepted 13 March 2014; Published 14 April 2014

Academic Editor: Shein-chung Chow

Copyright © 2014 Grant H. Skrepnek and Ashok Sahai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Within the context of clinical and other scientific research, a substantial need exists for an accurate determination of the point estimate in a lognormal mean model, given that highly skewed data are often present. As such, logarithmic transformations are often advocated to achieve the assumptions of parametric statistical inference. Despite this, existing approaches that utilize only a sample’s mean and variance may not necessarily yield the most efficient estimator. The current investigation developed and tested an improved efficient point estimator for a lognormal mean by capturing more complete information via the sample’s coefficient of variation. Results of an empirical simulation study across varying sample sizes and population standard deviations indicated relative improvements in efficiency of up to 129.47 percent compared to the usual maximum likelihood estimator and up to 21.33 absolute percentage points above the efficient estimator presented by Shen and colleagues (2006). The relative efficiency of the proposed estimator increased particularly as a function of decreasing sample size and increasing population standard deviation.