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Unification of the Fréchet and Weibull Distribution

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Author Info
Peter ter Berg
Abstract

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.

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Publisher Info
Paper provided by Netherlands Central Bank, Research Department in its series DNB Working Papers with number 198.

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Date of creation: Jan 2009
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Handle: RePEc:dnb:dnbwpp:198

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

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April. [Downloadable!] (restricted)
  2. Dorfman, Robert, 1979. "A Formula for the Gini Coefficient," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 146-49, February. [Downloadable!] (restricted)
  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 1211-15, September. [Downloadable!] (restricted)
  4. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November. [Downloadable!] (restricted)
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