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On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

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Abstract

The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this analytic bias correction outperforms a correction based on the parametric bootstrap. Three examples with actual data illustrate the application of our methods.

Suggested Citation

  • David E. Giles & Hui Feng & Ryan T. Godwin, 2011. "On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution," Econometrics Working Papers 1104, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:1104
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp1104.pdf
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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

    More about this item

    Keywords

    Maximum likelihood estimator; bias reduction; Lomax distribution; Pareto II distribution; bootstrap;
    All these keywords.

    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
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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