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 (${\hat{\mu }}_{B{C}_1}$, ${\hat{\mu }}_{B{C}_2}$, ${\hat{\mu }}_{B{C}_3}$, and ${\hat{\mu }}_{B{C}_4}$) are developed based on its MLE-like estimator. The second bias-corrected estimator ${\hat{\mu }}_{B{C}_2}$ is asymptotically unbiased and consequently, the third one ${\hat{\mu }}_{B{C}_3}$ and fourth one ${\hat{\mu }}_{B{C}_4}$ are also asymptotically unbiased because they are the approximations of the ${\hat{\mu }}_{B{C}_2}$. Simulation studies and a real data example suggest that four bias-corrected estimators, especially the latter three, significantly improve the small-sample performance.

Nakagami发行版广泛应用于通信工程，医学成像，多媒体等各个领域。通过广义的Nakagami分布的似然函数，针对Nakagami参数，提出了一种新的MLE估计形式的闭式估计量，其中广义Nakagami分布包含Nakagami分布作为特例。对于Nakagami分布的类似MLE的估计量，尺度参数（$\omega$）估计器与其最大似然估计器（MLE）和形状参数（$\mu$）估算器的效果接近相应的MLE。在大样本中证实了MLE样估计量的强一致性和渐近正态性。为了减少小尺寸样本中的偏差，请使用形状参数的四个偏差校正估计器（${\hat{\mu }}_{乙C_{\mathrm{1个}}}$， ${\hat{\mu }}_{乙C_2}$， ${\hat{\mu }}_{乙C_3}$和 ${\hat{\mu }}_{乙C_4}$）是根据类似MLE的估算器开发的。第二个偏差校正的估算器${\hat{\mu }}_{乙C_2}$ 是渐近无偏的，因此，第三个 ${\hat{\mu }}_{乙C_3}$ 和第四 ${\hat{\mu }}_{乙C_4}$ 也是渐近无偏的，因为它们是 ${\hat{\mu }}_{乙C_2}$。仿真研究和一个真实的数据示例表明，四个偏差校正的估计量，尤其是后三个，大大改善了小样本性能。