IDEAS home Printed from https://ideas.repec.org/a/tsj/stataj/v10y2010i3p482-495.html
   My bibliography  Save this article

Speaking Stata: The limits of sample skewness and kurtosis

Author

Listed:
  • Nicholas J. Cox

    (Durham University, UK)

Abstract

Sample skewness and kurtosis are limited by functions of sample size. The limits, or approximations to them, have repeatedly been rediscovered over the last several decades, but nevertheless seem to remain only poorly known. The limits impart bias to estimation and, in extreme cases, imply that no sample could bear exact witness to its parent distribution. The main results are explained in a tutorial review, and it is shown how Stata and Mata may be used to confirm and explore their consequences.

Suggested Citation

  • Nicholas J. Cox, 2010. "Speaking Stata: The limits of sample skewness and kurtosis," Stata Journal, StataCorp LP, vol. 10(3), pages 482-495, September.
    • Handle: RePEc:tsj:stataj:v:10:y:2010:i:3:p:482-495
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj10-3/st0204/
    as

    Download full text from publisher

    File URL: http://www.stata-journal.com/article.html?article=st0204
    File Function: link to article download
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nicholas J. Cox, 2005. "Speaking Stata: The protean quantile plot," Stata Journal, StataCorp LP, vol. 5(3), pages 442-460, September.
    2. Anna M. Fiori & Michele Zenga, 2009. "Karl Pearson and the Origin of Kurtosis," International Statistical Review, International Statistical Institute, vol. 77(1), pages 40-50, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Giovanni Campisi & Luca La Rocca & Silvia Muzzioli, 2023. "Assessing skewness in financial markets," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 48-70, February.
    2. J. Martin van Zyl, 2018. "An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions," Papers 1811.00476, arXiv.org, revised Nov 2018.
    3. Hui Tian & Andrew Yim & David P. Newton, 2021. "Tail-Heaviness, Asymmetry, and Profitability Forecasting by Quantile Regression," Management Science, INFORMS, vol. 67(8), pages 5209-5233, August.
    4. Balvers, Ronald J. & McDonald, Bill, 2021. "Designing a global digital currency," Journal of International Money and Finance, Elsevier, vol. 111(C).
    5. Garcia Pires, Armando J. & Skjeret, Frode, 2023. "Screening for partial collusion in retail electricity markets," Energy Economics, Elsevier, vol. 117(C).

    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. J. Martin van Zyl, 2018. "An Empirical Study of the Behaviour of the Sample Kurtosis in Samples from Symmetric Stable Distributions," Papers 1811.00476, arXiv.org, revised Nov 2018.
    2. Claudio Giovanni Borroni & Lucio De Capitani, 2022. "Some measures of kurtosis and their inference on large datasets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 573-607, December.
    3. Anna Maria Fiori, 2020. "On firm size distribution: statistical models, mechanisms, and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 447-482, September.
    4. Eugene Seneta, 2009. "Karl Pearson in Russian Contexts," International Statistical Review, International Statistical Institute, vol. 77(1), pages 118-146, April.
    5. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.
    6. Claudio Giovanni Borroni, 2009. "Understanding Karl Pearson's Influence on Italian Statistics in the Early 20th Century," International Statistical Review, International Statistical Institute, vol. 77(1), pages 81-95, April.
    7. Nicholas J. Cox, 2010. "Speaking Stata: Graphing subsets," Stata Journal, StataCorp LP, vol. 10(4), pages 670-681, December.
    8. Yeboah Asuamah, Samuel, 2015. "An econometric modelling of government activities-total energy demand nexus for Ghana," MPRA Paper 83489, University Library of Munich, Germany.

    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:tsj:stataj:v:10:y:2010:i:3:p:482-495. 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: Christopher F. Baum or Lisa Gilmore (email available below). General contact details of provider: http://www.stata-journal.com/ .

    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.