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There is a post about Satterthwaite approximation here: Proof and precise formulation of Welch-Satterthwaite equation.

However what I need to know but I can't find in above post is as follow:

If we want compute PDF of sum of gamma random variables with different scale parameters (same shape parameter) one way is using Satterthwaite approximation, but I can find nowhere about the limit of this approximation, I mean until what constraint this approx. can be true? my simulation shows when the number of gamma random variables that are supposed to add goes large, the approximated PDF deviates from simulation ! can anyone help please? my question is only about Satterthwaite approximation limit since I know we have some other solution to find even exact PDF of sum of gamma random variables in general case.

StubbornAtom
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A. R.
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  • It's worth to mention that above post that I referred, is just about an introduction of satterthwaite procedure while this post here: "Generic sum of Gamma random variables" is directly related about what I said. – A. R. Jul 21 '20 at 20:30
  • for more information here: section 4 at "http://www-personal.umd.umich.edu/~fmassey/gammaRV/" – A. R. Jul 21 '20 at 21:26

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