IDEAS home Printed from https://ideas.repec.org/p/zbw/faucse/892010.html
   My bibliography  Save this paper

Quasi-arithmetische Mittelwerte und Normalverteilung

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/64863/1/726472727.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    2. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-30, Tilburg University, Center for Economic Research.
    3. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Other publications TiSEM d8c37ad3-f9a5-4824-986d-2, Tilburg University, School of Economics and Management.
    4. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    5. Javier Martínez Torres & Jorge Pastor Pérez & Joaquín Sancho Val & Aonghus McNabola & Miguel Martínez Comesaña & John Gallagher, 2020. "A Functional Data Analysis Approach for the Detection of Air Pollution Episodes and Outliers: A Case Study in Dublin, Ireland," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    6. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.
    7. Xurxo Rigueira & María Araújo & Javier Martínez & Paulino José García-Nieto & Iago Ocarranza, 2022. "Functional Data Analysis for the Detection of Outliers and Study of the Effects of the COVID-19 Pandemic on Air Quality: A Case Study in Gijón, Spain," Mathematics, MDPI, vol. 10(14), pages 1-27, July.
    8. Martín, J. & Pérez, C.J., 2009. "Bayesian analysis of a generalized lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1377-1387, February.
    9. Bhupendra Singh & K. Sharma & Shubhi Rathi & Gajraj Singh, 2012. "A generalized log-normal distribution and its goodness of fit to censored data," Computational Statistics, Springer, vol. 27(1), pages 51-67, March.
    10. García, Victoriano J. & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2014. "On Modelling Insurance Data by Using a Generalized Lognormal Distribution || Sobre la modelización de datos de seguros usando una distribución lognormal generalizada," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 18(1), pages 146-162, December.
    11. Tzong-Ru Tsai & Yuhlong Lio & Ya-Yen Fan & Che-Pin Cheng, 2022. "Bias Correction Method for Log-Power-Normal Distribution," Mathematics, MDPI, vol. 10(6), pages 1-19, March.

    More about this item

    Keywords

    ML-estimator; quasi-arithmetic mean; exponential family; generalized logarithmic distribution; inverse transformed normal distribution;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:faucse:892010. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vierlde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.