IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v68y2000i2p137-153.html
   My bibliography  Save this article

The Early History of the Cumulants and the Gram‐Charlier Series

Author

Listed:
  • Anders Hald

Abstract

The early history of the Gram‐Charlier series is discussed from three points of view: (1) a generalization of Laplace's central limit theorem, (2) a least squares approximation to a continuous function by means of Chebyshev‐Hermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions. Thiele defined the cumulants in terms of the moments, first by a recursion formula and later by an expansion of the logarithm of the moment generating function. He devised a differential operator which adjusts any cumulant to a desired value. His little known 1899 paper in Danish on the properties of the cumulants is translated into English in the Appendix.

Suggested Citation

  • Anders Hald, 2000. "The Early History of the Cumulants and the Gram‐Charlier Series," International Statistical Review, International Statistical Institute, vol. 68(2), pages 137-153, August.
    • Handle: RePEc:bla:istatr:v:68:y:2000:i:2:p:137-153
    DOI: 10.1111/j.1751-5823.2000.tb00318.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1751-5823.2000.tb00318.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1751-5823.2000.tb00318.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiménez, Inés & Mora-Valencia, Andrés & Perote, Javier, 2022. "Semi-nonparametric risk assessment with cryptocurrencies," Research in International Business and Finance, Elsevier, vol. 59(C).
    2. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    3. Asmussen, Søren & Bladt, Mogens, 2022. "Moments and polynomial expansions in discrete matrix-analytic models," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1165-1188.
    4. Inés Jiménez & Andrés Mora-Valencia & Trino-Manuel Ñíguez & Javier Perote, 2020. "Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies," Mathematics, MDPI, vol. 8(12), pages 1-24, November.

    More about this item

    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:bla:istatr:v:68:y:2000:i:2:p:137-153. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.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.