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Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution

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  • Yilmaz, Hulya
  • Sazak, Hakan S.

Abstract

The generalized gamma distribution (GGD) is a very popular distribution since it includes many well known distributions. Estimation of the parameters of the GGD is quite problematic because of the complicated structure of its density function. We introduce two new estimation methods called maximum likelihood with goodness of fit test (MLGOFT) and double-looped maximum likelihood (ML) estimation. We show through simulations under several situations that the MLGOFT method is more efficient than the Method of Moments with goodness of fit test (MMGOFT) technique especially for small and moderate sample sizes whereas the double-looped ML is the superior estimation method for all cases. The double-looped ML method is also very fast, practical and straightforward.

Suggested Citation

  • Yilmaz, Hulya & Sazak, Hakan S., 2014. "Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 18-30.
    • Handle: RePEc:eee:matcom:v:98:y:2014:i:c:p:18-30
    DOI: 10.1016/j.matcom.2013.12.001
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    References listed on IDEAS

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    1. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    2. 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.
    3. Hirose, Hideo, 2000. "Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 81-97.
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    1. Volkan Soner Özsoy & Mehmet Güray Ünsal & H. Hasan Örkcü, 2020. "Use of the heuristic optimization in the parameter estimation of generalized gamma distribution: comparison of GA, DE, PSO and SA methods," Computational Statistics, Springer, vol. 35(4), pages 1895-1925, December.
    2. 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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