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A characterization of multivariate normal distribution and its application |
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| Authors: | Zhen-Hai Yang Kai-Tai Fang Jia-Juan Liang |
| Affiliation: | a Institute of Statistics, Beijing Polytechnic University, Beijing 100021, China b Statistics Research and Consultancy unit, Hong Kong Baptist University, Kowloon Tong, Hong Kong c Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China |
| 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. |
| Keywords: | Characterization of multinormality Multivariate normal distribution spherical distribution |
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