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Easy Estimation by a New Parameterization in the Three-Parameter Lognormal Distribution
en
Komori Yoshio
Hirose Hideo
A new computing method is proposed for the primary relative maximum of thelikelihood function in the three parameter lognormal distribution In the methodthe distribution is transformed to the extended lognormal distribution and thethree parameter estimation problems for the extended distribution are changed totwo parameter estimation problems which demand to maximize an object functionof the two parameters Since the function goes to +∞ only if both parameterssimultaneously go to +∞ or -∞ the two parameter estimation problems can beexpected to avoid computational di culties caused by the non regularity of the like lihood function in the lognormal distribution In addition since the employment ofgraphical tools makes it possible to easily nd proper initial guesses given to iterativemethods in the two parameter problem the combination of the reparameterizationand graphical tools is a simple but highly e ective method to cope with cases wherethe selection of the initial guess is di cult In the present article furthermore the analysis of the object function is given and the properties of the estimator areinvestigated in simulations Some examples are given for illustration
[Remark] Most of the material in this report has been superseded by the following paper: Y. Komori and H. Hirose (2004), Easy estimation by a new parameterization for the three-parameter lognormal distribution, J. Statistical Computation and Simulation, 74(1), 63-74.
Technical Report in Computer Science and Systems Engineering
2001-06-07
九州工業大学
1344-8803
Department of Control Engineering and Science, Kyushu Institute of Technology
九州工業大学情報工学部 制御システム工学科
https://doi.org/10.1080/0094965031000104341
Technical Report