A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation

It is well known that the inclusion of the threshold parameter in a lognormal distribution creates serious complications for parameter estimation; several parameterized schemes and global optimization procedures have been proposed to solve the problem in the maximum likelihood framework. A global Simulated Annealing optimization heuristic is proposed to solve the problem of maximum likelihood estimation in any parameterization scheme for the three-parameter lognormal distribution, as well as for the extended lognormal distribution. Positively and negatively skewed lognormal distributions are considered by introducing a one-parameter conditional estimation procedure in the classical parameterization for the three-parameter lognormal distribution, and a dual reparameterization is introduced for parameters estimation in the extended lognormal distribution. Simulated and real data are analyzed to test the efficiency of the proposed algorithm.