If you have $\frac{X}{X+Y}$ where X and Y are both independent Gamma distributions where $\alpha$ for both X and Y is different, but $\beta$ is the same for both, then how would that be different from the pdf for $\frac{X}{X+Y}$ where alpha is the same but beta is different?

The first scenario is given at the top of this pdf http://www.math.wm.edu/~leemis/chart/UDR/PDFs/GammaBeta.pdf

  • $\begingroup$ won't be answerable only from knowledge of the marginal distributions; you need to know the joint distribution. $\endgroup$ – Glen_b Oct 26 '16 at 11:26
  • $\begingroup$ Sorry I forgot to mention that these are independent variables and therefore the joint distribution is easily obtainable. $\endgroup$ – gorge Oct 26 '16 at 11:43
  • $\begingroup$ Please make sure that information needed to answer the question is made clear in the question. i.e. please edit your question $\endgroup$ – Glen_b Oct 26 '16 at 20:28
  • $\begingroup$ Is this the solution? math.stackexchange.com/a/190695 $\endgroup$ – gorge Oct 27 '16 at 6:37
  • $\begingroup$ Yes, it is! ..... $\endgroup$ – kjetil b halvorsen Oct 1 '17 at 15:10

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