Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution

摘要

Maximum likelihood parameter estimation becomes easy by augmenting the parameterspace of the probability distribution. A newly proposed extended model of thefour-parameter generalized gamma distribution includes the three-parameter generalizedextreme-value distribution which includes the two-parameter Gumbel distribution. Theserelationships allow us to construct the maximum likelihood parameter estimation procedurefrom simpler models to more complex models. This method works successfully whenthe solution is located in the interior of the parameter space. The continuation method isused for the model augmentation. The likelihood equations for the four-parameter generalizedgamma distribution does not always have solutions in the interior of the parameterspace; the continuation method, however, leads us to find solutions on the boundary or atthe corner of the parameter space.