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

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  • Arnold, Barry C.
  • Villasenor, Jose A.

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.

Suggested Citation

  • Arnold, Barry C. & Villasenor, Jose A., 2013. "On orthogonality of (X+Y) and X/(X+Y) rather than independence," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 584-587.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:584-587
    DOI: 10.1016/j.spl.2012.10.035
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    References listed on IDEAS

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    1. 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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