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

Maximum likelihood parameter estimation becomes easy by augmenting the parameter space of the probability distribution. A newly proposed extended model of the four-parameter generalized gamma distribution includes the three-parameter generalized extreme-value distribution which includes the two-parameter Gumbel distribution. These relationships allow us to construct the maximum likelihood parameter estimation procedure from simpler models to more complex models. This method works successfully when the solution is located in the interior of the parameter space. The continuation method is used for the model augmentation. The likelihood equations for the four-parameter generalized gamma distribution does not always have solutions in the interior of the parameter space; the continuation method, however, leads us to find solutions on the boundary or at the corner of the parameter space.