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Unification of the Fréchet and Weibull Distribution


  • Peter ter Berg


Well-known results for the Fréchet and Weibull distribution are streamlined using a unifying parametrisation. Expected values for order statistics follow through a fractional matrix power and the likelihood surface in case of a loglinear specification for the scale parameter is shown to have just two stationary points.

Suggested Citation

  • Peter ter Berg, 2009. "Unification of the Fréchet and Weibull Distribution," DNB Working Papers 198, Netherlands Central Bank, Research Department.
  • Handle: RePEc:dnb:dnbwpp:198

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    References listed on IDEAS

    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Dorfman, Robert, 1979. "A Formula for the Gini Coefficient," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 146-149, February.
    3. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, vol. 46(5), pages 1211-1215, September.
    4. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
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    More about this item


    Fréchet; Weibull; Gumbel; incomplete Gamma; Lorenz curve; order statistics; fractional matrix power; maximum likelihood.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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