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April, 1971 A Characterization of the Multivariate Normal Distribution
Mary R. Anderson
Ann. Math. Statist. 42(2): 824-827 (April, 1971). DOI: 10.1214/aoms/1177693441


In this paper we characterize the multivariate normal distribution through the mean vector of the distribution. In Theorem 3, we find that the multivariate normal distribution can also be characterized through its variance, even though unknown, provided the variance-covariance matrix is free of the parameter involved. We are able to determine the mean vector to within two unknowns, the variance-covariance matrix and a constant vector.


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Mary R. Anderson. "A Characterization of the Multivariate Normal Distribution." Ann. Math. Statist. 42 (2) 824 - 827, April, 1971.


Published: April, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0218.60019
MathSciNet: MR478465
Digital Object Identifier: 10.1214/aoms/1177693441

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 2 • April, 1971
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