Y. Komori and H. Hirose (2001), Easy estimation by a new parameterization in the three-parameter lognormal distribution, Technical Report CSSE-16, Faculty of Computer Science & Systems Engineering, Kyushu Institute of Technology.

Abstract
A new computing method is proposed for the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. In the method the distribution is transformed to the extended lognormal distribution, and the three-parameter estimation problems for the extended distribution are changed to two-parameter estimation problems, which demand to maximize an object function of the two parameters. Since the function goes to $+\infty$ only if both parameters simultaneously go to $+\infty$ or $-\infty$, the two-parameter estimation problems can be expected to avoid computational difficulties caused by the non-regularity of the likelihood function in the lognormal distribution. In addition, since the employment of graphical tools makes it possible to easily find proper initial guesses given to iterative methods in the two-parameter problem, the combination of the reparameterization and graphical tools is a simple but highly effective method to cope with cases where the selection of the initial guess is difficult. In the present article, furthermore, the analysis of the object function is given, and the properties of the estimator are investigated in simulations. Some examples are given for illustration.

Note
Most of the material in this report has been superseded by Y. Komori and H. Hirose (2004). Only a part of Subsection 3.3 in the report is still current. The part shows a necessary condition in relation to the selection of an initial guess for the continuation method. In addition, it gives some examples in which it is difficult to give an initial guess for the method.

The pdf file is obtainable from here.

Up

Last updated: 2003/11/20