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On parameter estimation for Amoroso family of distributions

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  • Combes, Catherine
  • Ng, Hon Keung Tony

Abstract

The four-parameter generalized gamma (GΓ) distribution, also known as the Amoroso family of distributions, is a flexible and versatile statistical distribution that encapsulates many well-known lifetime distributions, including the exponential, Weibull, lognormal, and gamma distributions as special instances. The four-parameter GΓ distribution is shown to be appropriate for fitting skewed and heavy-tailed data sets. However, even though the GΓ distribution is very useful and flexible, it remains less studied than its counterparts, probably due to the difficulty in estimating the parameters of the distribution. In this paper, we explore several novel iterative parameter estimation approaches for the four-parameter GΓ distribution, which includes the maximum likelihood estimation and minimum distance estimation approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:309-327
    DOI: 10.1016/j.matcom.2021.07.004
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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.
    2. Bucher, Axel & Segers, Johan, 2017. "On the maximum likelihood estimator for the Generalized Extreme-Value distribution," LIDAM Reprints ISBA 2017039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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.
    4. Suvra Pal & Hongbo Yu & Zachary D. Loucks & Ian M. Harris, 2020. "Illustration of the Flexibility of Generalized Gamma Distribution in Modeling Right Censored Survival Data: Analysis of Two Cancer Datasets," Annals of Data Science, Springer, vol. 7(1), pages 77-90, March.
    5. Hirose, Hideo, 1995. "Maximum likelihood parameter estimation in the three-parameter gamma distribution," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 343-354, October.
    6. Bassetti, Federico & Bodini, Antonella & Regazzini, Eugenio, 2006. "On minimum Kantorovich distance estimators," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1298-1302, July.
    7. 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.
    8. Delignette-Muller, Marie Laure & Dutang, Christophe, 2015. "fitdistrplus: An R Package for Fitting Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i04).
    9. 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.
    10. Marie Laure Delignette-Muller & Christophe Dutang, 2015. "fitdistrplus : An R Package for Fitting Distributions," Post-Print hal-01616147, HAL.
    11. 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.
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