A Remark on Cramer’s Theorem on the Decomposition of the Normal Law

H. Cramer's theorem is shown to be an equivalent of a particular case of Skitovich-Darmois' theorem on the independence of linear statistics. This means that each one of these theorems can be deduced from the other by a short elementary argument.

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Bibliographic Details
Published in:Theory of probability and its applications 1956-10, Vol.1 (4), p.435-436
Main Author: Linnik, Yu. V.
Format: Article
Language:English
Subjects:
Decomposition
Markov analysis
Normal distribution
Probability
Random variables
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Summary:H. Cramer's theorem is shown to be an equivalent of a particular case of Skitovich-Darmois' theorem on the independence of linear statistics. This means that each one of these theorems can be deduced from the other by a short elementary argument.
ISSN:0040-585X
1095-7219
DOI:10.1137/1101033