EXTENDED PATTERN SEARCH WITH TRANSFORMATIONS FOR THE 3-PARAMETER WEIBULL MLE PROBLEM

This study extends a method (pattern search) which was successfully used by the author for obtaining joint MLE (Maximum Likelihood Estimates) of all three Weibull parameters. Fifteen different transformations (to eliminate bounds) and three search direction approaches (derivative-free, exact and numerical gradient) of a revised unconstrained pattern search are evaluated on a set of randomly generated realistic test problems. Performance criteria include computation speed, accuracy of estimators (relatively to the true parameters and true MLEs), log-likelihood value achieved, and goodness of fit of the estimated distribution (to the sample or generating population). The results are analyzed statistically and successful (unsuccessful) transformation/direction options are identified for each criterion.