Abstract
We explore computational aspects of likelihood maximization for the generalized gamma (GG) distribution. We formulate a version of the score equations such that the equations involved are individually uniquely solvable. We observe that the resulting algorithm is well-behaved and competitive with the application of standard optimisation procedures. We also show that a somewhat neglected alternative existing approach to solving the score equations is good too, at least in the basic, three-parameter case. Most importantly, we argue that, in practice far from being problematic as a number of authors have suggested, the GG distribution is actually particularly amenable to maximum likelihood estimation, by the standards of general three- or more-parameter distributions. We do not, however, make any theoretical advances on questions of convergence of algorithms or uniqueness of roots.
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Noufaily, A., Jones, M.C. On maximization of the likelihood for the generalized gamma distribution. Comput Stat 28, 505–517 (2013). https://doi.org/10.1007/s00180-012-0314-4
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DOI: https://doi.org/10.1007/s00180-012-0314-4