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Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions

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  • Xiao Ling
  • David E. Giles

Abstract

We derive analytic expressions for the biases, to O(n− 1), of the maximum likelihood estimators of the parameters of the generalized Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap.

Suggested Citation

  • Xiao Ling & David E. Giles, 2014. "Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1778-1792, April.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:8:p:1778-1792
    DOI: 10.1080/03610926.2012.675114
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    1. Meagher Kieron J & Teo Ernie G.S. & Wang Wen, 2008. "A Duopoly Location Toolkit: Consumer Densities Which Yield Unique Spatial Duopoly Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-23, April.
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    3. Beenstock, Michael, 1995. "The stochastic economics of windpower," Energy Economics, Elsevier, vol. 17(1), pages 27-37, January.
    4. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    5. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Bias-Corrected MLEs
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-01 21:03:00

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    Cited by:

    1. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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