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Unification of the Fr�chet and Weibull Distribution

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  • Peter ter Berg
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    Abstract

    Well-known results for the Fr�chet 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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    File URL: http://www.dnb.nl/binaries/Working%20paper%20198_tcm46-211051.pdf
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    Bibliographic 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: Fr�chet; Weibull; Gumbel; incomplete Gamma; Lorenz curve; order statistics; fractional matrix power; maximum likelihood.;

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
    2. 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.
    3. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-39, November.
    4. Dorfman, Robert, 1979. "A Formula for the Gini Coefficient," The Review of Economics and Statistics, MIT Press, vol. 61(1), pages 146-49, February.
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