Improved Maximum Likelihood Estimation of the Shape Parameter in the Nakagami Distribution

We develop and evaluate analytic and bootstrap bias-corrected maximum likelihood estimators for the shape parameter in the Nakagami distribution. This distribution is widely used in a variety of disciplines, and the corresponding estimator of its scale parameter is trivially unbiased. We find that both “corrective” and “preventive” analytic approaches to eliminating the bias, to O(n-2), are equally, and extremely, effective and simple to implement. As a bonus, the sizeable reduction in bias comes with a small reduction in mean squared error. Overall, we prefer analytic bias corrections in the case of this estimator. This preference is based on the relative computational costs and the magnitudes of the bias reductions that can be achieved in each case. Our results are illustrated with two real-data applications, including one which provides the first application of the Nakagami distribution to data for ocean wave heights.