CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2010, 26(3) 234-244 DOI:      ISSN: 1001-4268 CN: 31-1256

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Keywords
Multinormal distribution
beta distribution
Chi squared distribution.
Authors
PubMed

VDR Conditional Tests for Multivariate Normality

Su Yan,Yang Zhenghai

School of Mathematics and Physics,
North China Electric Power University,College of Applied Science,
Beijing University of Technology

Abstract��

The $\chi^{2}$ conditional test for
multivariate normality is suggested. The transformed sample
$\mathbf{Y}_{d}=R\mathbf{V}_{d}$ from a $d$-variate normal
distribution has a symmetric multivariate Pearson type II
distribution, the result that $R^{2}$ has a beta distribution is
proved, the asymptotic Chi squared distribution of the statistic
$\chi^{2}$ based on beta distribution and sphere uniform
distribution is obtained. The Monte Carlo power study for
multivariate normality suggests that our test is a powerful
competitor to existing tests. The goodness-of-fit for multivariate
normality of iris data is analyzed.

Keywords�� Multinormal distribution   beta distribution   Chi squared distribution.  
Received 1900-01-01 Revised 1900-01-01 Online:  
DOI:
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Corresponding Authors: Su Yan
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