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Metrika

, Volume 31, Issue 1, pp 77–83 | Cite as

Best unbiased estimators for the parameters of a two-parameter Pareto distribution

  • S. K. Saksena
  • A. M. Johnson
Publication

Summary

For a two-parameter Pareto distributionMalik [1970] has shown that the maximum likelihood estimators of the parameters are jointly sufficient. In this article the maximum likelihood estimators are shown to be jointly complete. Furthermore, unbiased estimators for the two parameters are obtained and are shown to be functions of the jointly complete sufficient statistics, thereby establishing them as the best unblased estimators of the two parameters.

Keywords

Maximum Likelihood Estimator Unbiased Estimator Pareto Distribution Exponential Family Positive Skewness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Cramer, H.: Mathematical Methods of Statistics. Princeton, NJ, 1946.Google Scholar
  2. Johnson, N.L., andS. Kotz: Continuous Univariate Distributions-1 Boston 1970.Google Scholar
  3. Malik, H.J.: Exact moments of order statistics from the Pareto distribution. Skandinavisk Aktuarietidskrift49, 1966, 144–157.MathSciNetMATHGoogle Scholar
  4. —: Estimation of the parameters of the Pareto distribution. Metrika15, 1970, 126–132.MathSciNetCrossRefMATHGoogle Scholar
  5. Quandt, R.E.: Old and new methods of estimation and the Pareto distribution. Metrika10, 1966, 56–82.MathSciNetCrossRefGoogle Scholar
  6. Steindl, J.: Random Processes and the Growth of Firms: A Study of the Pareto Law. New York 1965.Google Scholar
  7. Zacks, S.: The Theory of Statistical Inference. New York 1971.Google Scholar

Copyright information

© Physica-Verlag 1984

Authors and Affiliations

  • S. K. Saksena
    • 1
  • A. M. Johnson
    • 2
  1. 1.Department of Mathematical SciencesUniversity of North Carolina at WilmingtonWilmingtonUSA
  2. 2.Department of Mathematics and Computer ScienceUniversity of ArkansasLittle RockUSA

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