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

Jun Zhao, SungBum Kim and Hyoung-Moon Kim

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 185, issue C, 308-324

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.

Keywords: Closed-form estimator; Bias-corrected estimator; MLE; Nakagami distribution (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:185:y:2021:i:c:p:308-324

DOI: 10.1016/j.matcom.2020.12.026

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