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Quasi-arithmetische Mittelwerte und Normalverteilung

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  • Klein, Ingo

Abstract

J.M. Keynes (1911) shows how distributions look like for which the arithmetic, the geometric and the harmonic mean are most probable values. We propose a general class of distributions for which the quasi-arithmetic means are ML-estimators such that these distributions can be transformed into an normal or a truncated normal distribution. As special cases we get for example the generalized logarithmic distributions introduced by Chen (1995).

Suggested Citation

  • Klein, Ingo, 2012. "Quasi-arithmetische Mittelwerte und Normalverteilung," Discussion Papers 89/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:892010
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    References listed on IDEAS

    as
    1. Freeman, Jade & Modarres, Reza, 2006. "Inverse Box-Cox: The power-normal distribution," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 764-772, April.
    2. Chen, Gemai, 1995. "Generalized log-normal distributions with reliability application," Computational Statistics & Data Analysis, Elsevier, vol. 19(3), pages 309-319, March.
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    More about this item

    Keywords

    ML-estimator; quasi-arithmetic mean; exponential family; generalized logarithmic distribution; inverse transformed normal distribution;
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