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December, 1967 A Characterization of Normality
M. V. Tamhankar
Ann. Math. Statist. 38(6): 1924-1927 (December, 1967). DOI: 10.1214/aoms/1177698630


A probability distribution on an $n$-dimensional Euclidean space can be specified by giving either the joint distribution of the usual rectangular coordinates or by the joint distribution of the polar coordinates. The object of this note is to obtain a characterization of normality in terms of independence of these coordinates under suitable regularity conditions. Further, if we slightly relax these conditions we get a new class of distributions which includes the normal distribution.


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M. V. Tamhankar. "A Characterization of Normality." Ann. Math. Statist. 38 (6) 1924 - 1927, December, 1967.


Published: December, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0157.48703
MathSciNet: MR219114
Digital Object Identifier: 10.1214/aoms/1177698630

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 6 • December, 1967
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