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Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution

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  • Hirose, Hideo

Abstract

Maximum likelihood parameter estimation becomes easy by augmenting the parameter space of the probability distribution. A newly proposed extended model of the four-parameter generalized gamma distribution includes the three-parameter generalized extreme-value distribution which includes the two-parameter Gumbel distribution. These relationships allow us to construct the maximum likelihood parameter estimation procedure from simpler models to more complex models. This method works successfully when the solution is located in the interior of the parameter space. The continuation method is used for the model augmentation. The likelihood equations for the four-parameter generalized gamma distribution does not always have solutions in the interior of the parameter space; the continuation method, however, leads us to find solutions on the boundary or at the corner of the parameter space.

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  • 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.
    • Handle: RePEc:eee:matcom:v:54:y:2000:i:1:p:81-97
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    References listed on IDEAS

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    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    2. Hirose, Hideo, 1997. "Maximum likelihood parameter estimation in the three-parameter log-normal distribution using the continuation method," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 139-152, April.
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    Cited by:

    1. Han, Lili & Wu, Fangxiang & Sheng, Jie & Ding, Feng, 2012. "Two recursive least squares parameter estimation algorithms for multirate multiple-input systems by using the auxiliary model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 777-789.
    2. Hirose, Hideo, 2007. "The mixed trunsored model with applications to SARS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 443-453.
    3. 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.
    4. Cynthia Tojeiro & Francisco Louzada, 2012. "A general threshold stress hybrid hazard model for lifetime data," Statistical Papers, Springer, vol. 53(4), pages 833-848, November.
    5. 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.
    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.
    7. Park, Jeong-Soo, 2005. "A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(4), pages 227-234.
    8. Chen, Feiyan & Ding, Feng & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 53-67.

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