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A characterization of multivariate normal distribution and its application

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  • Yang, Zhen-Hai
  • Fang, Kai-Tai
  • Liang, Jia-Juan

Abstract

Let X1, X2, ..., Xn be i.i.d. d-dimensional random vectors with a continuous density. Let and . In this paper we find that the distribution of Zk (or Yk) can be used for characterizing multivariate normal distribution. This characterization can be employed for testing multivariate normality in terms of the so-called transformation method.

Suggested Citation

  • Yang, Zhen-Hai & Fang, Kai-Tai & Liang, Jia-Juan, 1996. "A characterization of multivariate normal distribution and its application," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 347-352, November.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:4:p:347-352
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    References listed on IDEAS

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    1. Romeu, J. L. & Ozturk, A., 1993. "A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 309-334, August.
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    Cited by:

    1. Liang, Jiajuan & Pan, William S.Y. & Yang, Zhen-Hai, 2004. "Characterization-based Q-Q plots for testing multinormality," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 183-190, December.

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