A characterization of multivariate normal distribution and its application

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

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

10 Citations (Scopus)


Let X1, X2, ⋯ ,Xn be i.i.d. d-dimensional random vectors with a continuous density. Let Sk = ∑ki = 1 XiXTi, Yk = Sk-1/2Xk and Zk = Yk/(√1 - YTk Yk) (k ≥ d). 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.

Original languageEnglish
Pages (from-to)347-352
Number of pages6
JournalStatistics and Probability Letters
Issue number4
Publication statusPublished - 15 Nov 1996
Externally publishedYes

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Characterization of multinormality
  • Multivariate normal distribution
  • Spherical distribution


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