On Pairwise and Mutual Independence: Characterizations of Rectangular Distributions

Examples are given of three absolutely continuous random variables X, Y, and Z, which are identically distributed, pairwise but not mutually independent, and for which Z is a simple function of X + Y. These are shown to provide characterizations of the absolutely continuous rectangular distributions...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1978-06, Vol.73 (362), p.432-433
Main Author: Driscoll, Michael F.
Format: Article
Language:English
Subjects:
Characterizations
Independence
Probability theory
Random variables
Rectangular distributions
Theory and Methods
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Summary:Examples are given of three absolutely continuous random variables X, Y, and Z, which are identically distributed, pairwise but not mutually independent, and for which Z is a simple function of X + Y. These are shown to provide characterizations of the absolutely continuous rectangular distributions. The results carry over to the discrete rectangular distributions.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1978.10481596