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On maximization of the likelihood for the generalized gamma distribution

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  • Angela Noufaily
  • M. Jones

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Angela Noufaily & M. Jones, 2013. "On maximization of the likelihood for the generalized gamma distribution," Computational Statistics, Springer, vol. 28(2), pages 505-517, April.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:505-517
    DOI: 10.1007/s00180-012-0314-4
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    References listed on IDEAS

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    1. Gomes, O. & Combes, C. & Dussauchoy, A., 2008. "Parameter estimation of the generalized gamma distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 955-963.
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    Cited by:

    1. Martínez-Ovando Juan Carlos & Olivares-Guzmán Sergio I. & Roldán-Rodríguez Adriana, 2014. "Predictive Inference on Finite Populations Segmented in Planned and Unplanned Domains," Working Papers 2014-04, Banco de México.
    2. Pedro L Ramos & Diego C Nascimento & Paulo H Ferreira & Karina T Weber & Taiza E G Santos & Francisco Louzada, 2019. "Modeling traumatic brain injury lifetime data: Improved estimators for the Generalized Gamma distribution under small samples," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-22, August.
    3. Angela Noufaily & M. C. Jones, 2013. "Parametric quantile regression based on the generalized gamma distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(5), pages 723-740, November.
    4. Adam Martin-Schwarze & Jarad Niemi & Philip Dixon, 2017. "Assessing the Impacts of Time-to-Detection Distribution Assumptions on Detection Probability Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 465-480, December.
    5. André Pereira & Bernardo Andrade, 2015. "On the genetic algorithm with adaptive mutation rate and selected statistical applications," Computational Statistics, Springer, vol. 30(1), pages 131-150, March.
    6. Combes, Catherine & Ng, Hon Keung Tony, 2022. "On parameter estimation for Amoroso family of distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 309-327.

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