IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v2y1984i5p263-267.html
   My bibliography  Save this article

A measure of skewness and kurtosis and a graphical method for assessing multivariate normality

Author

Listed:
  • Srivastava, M. S.

Abstract

Using principal components, a measure of skewness and kurtosis is developed for multivariate populations. The sample analogues of these measures are proposed as tests of multivariate normality. Also, a graphical method is presented for assessing multivariate normality.

Suggested Citation

  • Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:5:p:263-267
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(84)90062-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Abdi, Me’raj & Madadi, Mohsen & Balakrishnan, Narayanaswamy & Jamalizadeh, Ahad, 2021. "Family of mean-mixtures of multivariate normal distributions: Properties, inference and assessment of multivariate skewness," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    2. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    3. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    4. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    5. Wang, Jin, 2009. "A family of kurtosis orderings for multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 509-517, March.
    6. Wang, Jin & Zhou, Weihua, 2012. "A generalized multivariate kurtosis ordering and its applications," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 169-180.
    7. Jin Wang & Weihua Zhou, 2015. "Effect of kurtosis on efficiency of some multivariate medians," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 331-348, September.
    8. Kurita, Eri & Seo, Takashi, 2022. "Multivariate normality test based on kurtosis with two-step monotone missing data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    10. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    11. Takayuki Yamada & Tetsuto Himeno, 2019. "Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality," Computational Statistics, Springer, vol. 34(2), pages 911-941, June.
    12. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    13. Araújo, Tanya & Dias, João & Eleutério, Samuel & Louçã, Francisco, 2013. "A measure of multivariate kurtosis for the identification of the dynamics of a N-dimensional market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3708-3714.
    14. Balakrishnan, N. & Scarpa, Bruno, 2012. "Multivariate measures of skewness for the skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 73-87, February.
    15. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    16. Hea-Jung Kim, 2015. "A best linear threshold classification with scale mixture of skew normal populations," Computational Statistics, Springer, vol. 30(1), pages 1-28, March.
    17. Wangli Xu & Yanwen Li & Dawo Song, 2013. "Testing normality in mixed models using a transformation method," Statistical Papers, Springer, vol. 54(1), pages 71-84, February.
    18. Maruyama, Yosihito, 2007. "On Srivastava's multivariate sample skewness and kurtosis under non-normality," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 335-342, February.
    19. Tanya Araujo & João Dias & Samuel Eleutério & Francisco Louçã, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Working Papers Department of Economics 2012/21, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    20. Tanya Ara'ujo & Jo~ao Dias & Samuel Eleut'erio & Francisco Louc{c}~a, 2012. "How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market," Papers 1207.1202, arXiv.org.
    21. Baishuai Zuo & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions," Papers 2311.18176, arXiv.org.
    22. Kim, Hea-Jung, 2011. "Classification of a screened data into one of two normal populations perturbed by a screening scheme," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1361-1373, November.
    23. Hea-Jung Kim, 2015. "Segmented classification analysis with a class of rectangle-screened elliptical populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1877-1895, September.
    24. Kim, Namhyun, 2016. "A robustified Jarque–Bera test for multivariate normality," Economics Letters, Elsevier, vol. 140(C), pages 48-52.
    25. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.

    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:eee:stapro:v:2:y:1984:i:5:p:263-267. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.