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Closed-form estimators and bias-corrected estimators for the Nakagami distribution

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  • Zhao, Jun
  • Kim, SungBum
  • Kim, Hyoung-Moon

Abstract

The Nakagami distribution is widely applied in various areas such as communicational engineering, medical imaging, multimedia, among others. New MLE-like estimators in closed-form are proposed for the Nakagami parameters through the likelihood function of the generalized Nakagami distribution, which contains the Nakagami distribution as a special case. For the MLE-like estimators of the Nakagami distribution, the scale parameter (ω) estimator is the same as its maximum likelihood estimator (MLE) and the shape parameter (μ) estimator performs close to the corresponding MLE. Strong consistency and asymptotic normality of the MLE-like estimators are confirmed in large-size samples. To reduce the bias in the samples with small sizes, four bias-corrected estimators of the shape parameter (μˆBC1, μˆBC2, μˆBC3, and μˆBC4) are developed based on its MLE-like estimator. The second bias-corrected estimator μˆBC2 is asymptotically unbiased and consequently, the third one μˆBC3 and fourth one μˆBC4 are also asymptotically unbiased because they are the approximations of the μˆBC2. Simulation studies and a real data example suggest that four bias-corrected estimators, especially the latter three, significantly improve the small-sample performance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:308-324
    DOI: 10.1016/j.matcom.2020.12.026
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    References listed on IDEAS

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    1. Francisco Louzada & Pedro L. Ramos & Eduardo Ramos, 2019. "A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations," The American Statistician, Taylor & Francis Journals, vol. 73(2), pages 195-199, April.
    2. 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.
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    Cited by:

    1. Zhao, Jun & Jang, Yu-Hyeong & Kim, Hyoung-Moon, 2022. "Closed-form and bias-corrected estimators for the bivariate gamma distribution," Journal of Multivariate Analysis, Elsevier, vol. 191(C).

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