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ON THE CHARACTERIZATION OF NORMALITY FOR THE CLASS OF SPHERICAL DISTRIBUTIONS
Tea-Yuan Hwang, 黃提源, Chin-Yuan Hu and 胡金源
Chinese Journal of Mathematics
Vol. 24, No. 1 (MARCH 1996), pp. 47-54
Published by: Mathematical Society of the Republic of China
Stable URL: http://www.jstor.org/stable/43836621
Page Count: 8
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In this paper, a quite different proof has been provided to obtain the theorem: under the class of spherical distributions the independence of X̄ and S² (in standard notations) is equivalent to the random vector X̰ having multivariate normal distribution with zero mean and covariance matrix cḬ, where Ḭ is the identity matrix and c > 0 is a constant.
Chinese Journal of Mathematics © 1996 Mathematical Society of the Republic of China