On orthogonality of (X+Y) and X/(X+Y) rather than independence
If X and Y are independent and if X+Y and X/(X+Y) are independent random variables, then X and Y must have gamma distributions. To confirm that lack of correlation between X and X/(X+Y) does not characterize the gamma distribution, a large class of distributions are identified for which cov[X,X/(X+Y)]=0. A related question in the context of matrix-variate distributions is addressed.
Volume (Year): 83 (2013)
Issue (Month): 2 ()
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- Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
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