Skip to main content
SpringerLink
Log in

Measures of multivariate skewness and kurtosis for tests of nonnormality

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Measures of multivariate skewness and kurtosis are proposed that are based on the skewness and kurtosis of individual components of standardized sample vectors. Asymptotic properties and small sample critical values of tests for nonnormality based on these measures are provided. It is demonstrated that the tests have favorable power properties. Extensions to time series data are pointed out.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baringhaus L & N Henze (1988) A Consistent Test for Multivariate Normality Based on the Empirical Characteristic Function, Metrika, 35, 339–348.

    Article  MathSciNet  MATH  Google Scholar 

  • Bowman KO & LR Shenton (1975) Omnibus Contours for Departures From Normality Based on √b1 and b2, Biometrika, 62, 243–250.

    MathSciNet  MATH  Google Scholar 

  • D'Agostino RB & ES Pearson (1973) Tests for Departure from Normality. Empirical Results for the Distributions of b2 and √b1, Biometrika, 60, 613–622, Correction, Biometrika, (1974), 61, 647.

    MathSciNet  MATH  Google Scholar 

  • D'Agostino RB & GL Tietjen (1971) Simulation Probability Points of b2 for Small Samples, Biometrika, 58, 669–672.

    MATH  Google Scholar 

  • Gasser T (1975) Goodness-of-fit Tests for Correlated Data, Biometrika, 62, 563–570.

    Article  MathSciNet  MATH  Google Scholar 

  • Isogai T (1989) On Using Influence Functions for Testing Multivariate Normality, Annals of the Institute of Statistical Mathematics, 41, 169–186.

    MathSciNet  MATH  Google Scholar 

  • Jarque CM & AK Bera (1987) A Test for Normality of Observations and Regression Residuals, International Statistical Review, 55, 163–172.

    Article  MathSciNet  MATH  Google Scholar 

  • Lütkepohl H & W Schneider (1989) Testing for Nonnormality of Autoregressive Time Series, Computational Statistics Quarterly, 5, 151–168.

    MATH  Google Scholar 

  • Malkovich JF & AA Afifi (1973) On Tests for Multivariate Normality, Journal of the American Statistical Association, 68, 176–179.

    Article  Google Scholar 

  • Mardia KV (1970) Measures of Multivariate Skewness and Kurtosis with Applications, Biometrika, 57, 519–530.

    Article  MathSciNet  MATH  Google Scholar 

  • Mardia KV (1974) Applications of some Measures of Multivariate Skewness and Kurtosis for Testing Normality and Robustness Studies, Sankhyã, A 36, 115–128.

    MathSciNet  MATH  Google Scholar 

  • Mardia KV (1980) Tests for Univeriate and Multivariate Normality, Handbook of Statistics, Vol. I, Amsterdam, North-Holland, 279–320.

    Google Scholar 

  • Pearson ES RB D'Agostino & KO Bowman (1977) Tests for Departure From Normality: Comparison of Powers, Biometrika, 64, 231–246.

    Article  MATH  Google Scholar 

  • Rao CR (1973) Linear Statistical Inference and Its Applications, 2nd Ed., Wiley, New York.

    MATH  Google Scholar 

  • Rohatgi VK (1984) Statistical Inference, New York, John Wiley.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Statistik und Ökonometrie, Christian-Albrechts-Universität Kiel, Olshausenstr. 40, 2300, Kiel 1, Germany

    H. Lütkepohl & B. Theilen

Authors
  1. H. Lütkepohl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Theilen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lütkepohl, H., Theilen, B. Measures of multivariate skewness and kurtosis for tests of nonnormality. Statistical Papers 32, 179–193 (1991). https://doi.org/10.1007/BF02925492

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925492

Keywords

Search

Navigation