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.

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Year of publication:	2013
Authors:	Arnold, Barry C. ; Villasenor, Jose A.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 2, p. 584-587
Publisher:	Elsevier
Subject:	Characterization \| Covariance \| Uncorrelated \| Gamma distribution \| Matrix variate

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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