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Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations

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  • Zhi-Sheng Ye
  • Nan Chen

Abstract

It is well-known that maximum likelihood (ML) estimators of the two parameters in a gamma distribution do not have closed forms. This poses difficulties in some applications such as real-time signal processing using low-grade processors. The gamma distribution is a special case of a generalized gamma distribution. Surprisingly, two out of the three likelihood equations of the generalized gamma distribution can be used as estimating equations for the gamma distribution, based on which simple closed-form estimators for the two gamma parameters are available. Intuitively, performance of the new estimators based on likelihood equations should be close to the ML estimators. The study consolidates this conjecture by establishing the asymptotic behaviors of the new estimators. In addition, the closed-forms enable bias-corrections to these estimators. The bias-correction significantly improves the small-sample performance.

Suggested Citation

  • Zhi-Sheng Ye & Nan Chen, 2017. "Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations," The American Statistician, Taylor & Francis Journals, vol. 71(2), pages 177-181, April.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:2:p:177-181
    DOI: 10.1080/00031305.2016.1209129
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    Cited by:

    1. Tin Lok James Ng & Thomas Brendan Murphy, 2021. "Weighted stochastic block model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1365-1398, December.
    2. Zhao, Jun & Kim, SungBum & Kim, Hyoung-Moon, 2021. "Closed-form estimators and bias-corrected estimators for the Nakagami distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 308-324.
    3. Bruzda, Joanna, 2020. "Demand forecasting under fill rate constraints—The case of re-order points," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1342-1361.
    4. Hou, Hui & Tang, Junyi & Zhang, Zhiwei & Wang, Zhuo & Wei, Ruizeng & Wang, Lei & He, Huan & Wu, Xixiu, 2023. "Resilience enhancement of distribution network under typhoon disaster based on two-stage stochastic programming," Applied Energy, Elsevier, vol. 338(C).
    5. Victor Mooto Nawa & Saralees Nadarajah, 2023. "New Closed Form Estimators for the Beta Distribution," Mathematics, MDPI, vol. 11(13), pages 1-20, June.

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