IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v54y2000i1p81-97.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475400002019
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. Hirose, Hideo, 2007. "The mixed trunsored model with applications to SARS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 443-453.
    5. 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.
    6. 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.
    7. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
    2. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    3. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    4. Roberts, Leigh A., 2015. "Distribution free testing of goodness of fit in a one dimensional parameter space," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 215-222.
    5. Haitham M. Yousof & Yusra Tashkandy & Walid Emam & M. Masoom Ali & Mohamed Ibrahim, 2023. "A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
    6. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    7. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    8. Mukhtar M. Salah & M. El-Morshedy & M. S. Eliwa & Haitham M. Yousof, 2020. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    9. Raid Al-Aqtash & Avishek Mallick & G.G. Hamedani & Mahmoud Aldeni, 2021. "On the Gumbel-Burr XII Distribution: Regression and Application," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(6), pages 1-31, December.
    10. Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
    11. Ahmed Z. Afify & Haitham M. Yousof & Gauss M. Cordeiro & Edwin M. M. Ortega & Zohdy M. Nofal, 2016. "The Weibull Fréchet distribution and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2608-2626, October.
    12. Tu, Shiyi & Wang, Min & Sun, Xiaoqian, 2016. "Bayesian analysis of two-piece location–scale models under reference priors with partial information," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 133-144.
    13. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    14. Adelchi Azzalini & Monica Chiogna, 2004. "Some results on the stress–strength model for skew-normal variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 315-326.
    15. Yuanhua Feng & Wolfgang Karl Härdle, 2021. "Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression," Working Papers CIE 142, Paderborn University, CIE Center for International Economics.
    16. Joarder, Avijit & Krishna, Hare & Kundu, Debasis, 2011. "Inferences on Weibull parameters with conventional type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 1-11, January.
    17. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa Ç. Korkmaz & Munir Ahmad, 2018. "The transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-23, December.
    18. Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    19. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    20. Mohamed Ibrahim & Walid Emam & Yusra Tashkandy & M. Masoom Ali & Haitham M. Yousof, 2023. "Bayesian and Non-Bayesian Risk Analysis and Assessment under Left-Skewed Insurance Data and a Novel Compound Reciprocal Rayleigh Extension," Mathematics, MDPI, vol. 11(7), pages 1-26, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:54:y:2000:i:1:p:81-97. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.