Noufaily, Angela and Jones, M. C.
On maximization of the likelihood for the generalized gamma distribution.
Computational Statistics, 28 pp. 505–517.
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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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