On maximization of the likelihood for the generalized gamma distribution

Noufaily, Angela and Jones, M. C. (2012). On maximization of the likelihood for the generalized gamma distribution. Computational Statistics, 28 pp. 505–517.

DOI: https://doi.org/10.1007/s00180-012-0314-4

URL: http://www.springerlink.com/content/c9423m42r02216...


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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