hello people, I need some help with computational statistics:

I need to proof that :

if X~(a,t) and Y~(b,t) then X / ( X+Y) ~Beta(a,b)

( hint: I think I need to use the inverse transform method )

thanks !!!

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- Nov 13th 2006, 11:36 AMWeeGGenerating Random Variables
hello people, I need some help with computational statistics:

I need to proof that :

if X~(a,t) and Y~(b,t) then X / ( X+Y) ~Beta(a,b)

( hint: I think I need to use the inverse transform method )

thanks !!! - Nov 16th 2006, 08:02 AMCaptainBlack
Should be:

if $\displaystyle X\sim \Gamma(a,t)$ and $\displaystyle Y\sim \Gamma(b,t)$ then $\displaystyle X / ( X+Y) \sim \mbox{Beta}(a,b)$

See here section with equations 33-42.

RonL