On orthogonality of (X+Y) and X/(X+Y) rather than independence

Barry C. Arnold and Jose A. Villasenor

Statistics & Probability Letters, 2013, vol. 83, issue 2, 584-587

Abstract: 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.

Keywords: Characterization; Covariance; Uncorrelated; Gamma distribution; Matrix variate (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.10.035

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