|
|||||
|
|
CORRELATIONS AND CHARACTERIZATIONS OF THE UNIFORM DISTRIBUTION |
|
| Authors: | Timothy C Brown Donald I Cartwright G K Eagleson |
| Institution: | Department of Mathematics, Monash University;Department of Pure Mathematics, University of Sydney;CSIRO Division of Mathematics and Statistics, Australia |
| Abstract: | 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. |
| Keywords: | Characterization correlation coefficient Kendall's coefficient of concordance normal distribution Pearson's X |