Method of moment generating function with Gamma Distribution
Assume that is a sample space of size n from a gamma distribution population with and unknown.
Us the method of moment generating function to show that is a pivotal quantity and has a distribution with 4n df.
I know that the moment generating function of a Gamma Distribution is .
I attempted to replicate http://www.mathhelpforum.com/math-he...-function.html, but got nowhere. I figure it has to like:
since that's the mgf of a distribution with 4n df.