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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 14, Fasc. 2,
pages 257 - 263
 

ON THREE CHARACTERIZATIONS OF THE NORMAL DISTRIBUTION

M. P. Quine

Abstract: Of all the characterizations of the normal distribution, three landmarks are the theorems of Bernstein and Skitovitch concerning independence of linear forms and the theorem of Geary concerning independence of sample mean and variance. In this note, ideas from several proofs of these theorems are distilled to give unified proofs which depend mostly on simple probability and characteristic function concepts.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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