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

摘要

Maximum likelihood parameter estimation becomes easy by augmenting the parameterspace of the probability distribution. An extended model of the four-parameter generalizedgamma distribution includes the three-parameter generalized extreme-value distributionwhich includes the two-parameter Gumbel distribution. These relationships allow us toconstruct the maximum likelihood parameter estimation procedure from simpler models tomore complex models. This method works successfully when the solution is located in theinterior of the parameter space. The continuation method is used for the model augmentation.The likelihood equations for the four-parameter generalized gamma distribution doesnot 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 parameterspace.