  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.
