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Reducing bias of the maximum likelihood estimator of shape parameter for the gamma Distribution

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  • Jin Zhang

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. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Jin Zhang, 2013. "Reducing bias of the maximum likelihood estimator of shape parameter for the gamma Distribution," Computational Statistics, Springer, vol. 28(4), pages 1715-1724, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1715-1724
    DOI: 10.1007/s00180-012-0375-4
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    References listed on IDEAS

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    1. Tea-Yuan Hwang & Ping-Huang Huang, 2002. "On New Moment Estimation of Parameters of the Gamma Distribution Using its Characterization," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 840-847, December.
    2. T. Yanagimoto, 1988. "The conditional maximum likelihood estimator of the shape parameter in the gamma distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 161-175, December.
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