Y. Komori and H. Hirose (2004), Easy estimation by a new parameterization for the three-parameter lognormal distribution, Journal of Statistical Computation and Simulation, 74 (1), 63-74.

Abstract
A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter estimation problem to a two-parameter estimation problem on the basis of an extended lognormal distribution. The algorithm provides the way of seeking the profile of an object function in the two-parameter estimation problem. It is simple and numerically stable because it is constructed on the basis of the bisection method. The profile clearly and easily shows whether a primary relative maximum exists or not, and also gives a primary relative maximum certainly if it exists.

Note
The journal is abstracted/indexed in MathSciNet and Web of Science. Thus, additional information about the paper is obtainable from the databases.

The following are source files implimenting the algorithm proposed in the paper:

mainbisection_2p_for_simulation.c and mainbisection_2p_for_single_dataset.c

The pdf file is obtainable from here. (Access to the file will depend on your entitlements.) In addition, the accepted post peer review version of manuscript is obtainable from here.

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Last updated: 2013/11/18