On Maximisation of the Likelihood for the Generalised Gamma Distribution

We explore computational aspects of likelihood maximisation for the generalised gamma distribution. We improve on earlier work by being the first to formulate the iterative approach to solution of the likelihood score equations in such a way that the individual equations involved are uniquely solvable. We observe that the resulting algorithm is well-behaved and competitive with the application of standard optimisation procedures. Most importantly, we argue that, far from being problematic as a number of authors have suggested, the generalised gamma distribution is actually particularly amenable to maximum likelihood estimation, by the standards of general threeor more-parameter distributions.