Abstract
The gamma distribution is an important probability distribution in statistics. The maximum likelihood estimator (MLE) of its shape parameter is well known to be considerably biased, so that it has some modified versions. A new modified MLE of the shape for the gamma distribution is proposed in this paper, which is consistent, asymptotically normal and efficient. For finite-sample behavior, the new estimator improves the traditional MLE not only for reducing bias but also for gaining estimation efficiency significantly. In terms of estimation efficiency, it dominates other existing modified estimators.
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Acknowledgments
This research is supported by the Natural Science Foundation of China (NSFC, Grant No. 10871167, 1161054). The author would like to thank anonymous referees for their helpful comments and suggestions.
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Zhang, J. Reducing bias of the maximum likelihood estimator of shape parameter for the gamma Distribution. Comput Stat 28, 1715–1724 (2013). https://doi.org/10.1007/s00180-012-0375-4
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DOI: https://doi.org/10.1007/s00180-012-0375-4