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November 11th, 2017, 03:45 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Function of Two Independent Gammas follow Beta I've gotten so close but I cannot figure out for the life of me what's wrong. At the end, my PDF comes out to be: I'm literally off by the constant of theta. For my substitutions, I let U = X + Y and W = X/(X+Y) and my Jacobian came out to be u (after taking the absolute value). So then I just do the substitutions and multiply by the Jacobian, and I get what I have above... which is NOT the Beta Distribution PDF since I'm off by the constant of theta. Can somebody show me a proof of this so I can see where I'm going wrong? 
November 11th, 2017, 11:26 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,009 Thanks: 1042  
November 12th, 2017, 07:37 AM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
Thanks, I was just failing to do my integral substitutions properly. That's why my theta wasn't disappearing.


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beta, follow, function, gammas, independent 
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