Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution.

Jacob Schwartz, Ryan T. Godwin, David E. Giles

Research output: Contribution to journalArticlepeer-review


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, toO(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 the 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 the one which provides the first application of the Nakagami distribution to data for ocean wave heights.
Original languageEnglish
Pages (from-to)434-445
Number of pages12
JournalJournal of Statistical Computation and Simulation
Issue number3
StatePublished - 1 Mar 2013
Externally publishedYes


  • MAXIMUM likelihood statistics
  • PARAMETER estimation
  • DISTRIBUTION (Probability theory)
  • STATISTICAL bootstrapping
  • MONTE Carlo method
  • DATA analysis
  • OCEAN waves
  • bootstrap
  • maximum likelihood
  • Monte Carlo simulation


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