Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2012, Article ID 897106, 6 pages
Research Article

Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA

Received 29 February 2012; Revised 26 June 2012; Accepted 2 July 2012

Academic Editor: Xiaohu Li

Copyright © 2012 Zhenmin Chen and Feng Miao. 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.


The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.