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

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 (omega) estimator is the same as its maximum likelihood estimator (MLE) and the shape parameter (mu) 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 ((mu) over cap (BC1), (mu) over cap (BC2), (mu) over cap (BC3), and (mu) over cap (BC4)) are developed based on its MLE-like estimator. The second bias-corrected estimator (mu) over cap (BC2) is asymptotically unbiased and consequently, the third one (mu) over cap (BC3) and fourth one (mu) over cap (BC4) are also asymptotically unbiased because they are the approximations of the (mu) over cap (BC2). Simulation studies and a real data example suggest that four bias-corrected estimators, especially the latter three, significantly improve the small-sample performance. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.