Easy estimation by a new parameterization for
the three-parameter lognormal distribution
Authors
Komori Y, Hirose H
Source
Journal of Statistical Computation and Simulation, 74 (1): pp.63-74
(2004.1)
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.
Key Words
extended lognormal distribution, dimension reduction, primary
relative maximum, local maximum likelihood estimate, embedded
problem