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CORRELATIONS AND CHARACTERIZATIONS OF THE UNIFORM DISTRIBUTION
Author(s) -
Brown Timothy C.,
Cartwright Donald I.,
Eagleson G. K.
Publication year - 1986
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1986.tb00586.x
Subject(s) - independent and identically distributed random variables , pairwise independence , independence (probability theory) , pairwise comparison , mathematics , distribution (mathematics) , moment (physics) , product (mathematics) , space (punctuation) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , computer science , random variable , physics , statistics , geometry , sum of normally distributed random variables , classical mechanics , operating system
Summary Two characterizations of the uniform distribution on a suitable compact space are proved. These characterizations are applied to a number of particular examples of which the most interesting is the following: if X , Y and Z are independent n ‐vectors whose components are independent and identically distributed within a vector, then the pairwise independence of the product moment correlation coefficients between X , Y and Z implies that these vectors are normally distributed.