Hopefully an easy one. My apologies for not using math format, I am not sure how to do so.
I have a known Gamma distribution f(Y), say shape=3 and scale=2. I also know that that the distribution of f(Y)^1/2, i.e. the square root of f(Y), can be described as a Nakagami distribution f(X) where X=sqrt(Y). What I'm after is how to identify the parameters of that Nakagami distribution? I have found links describing how to go the other way (e.g https://handwiki.org/wiki/Nakagami_distribution) but it seems like the Omega parameter in that link is unknown in my case.
Through simulation and recovery I believe the answer is that the Nakagami shape parameter m is equal to the Gamma shape, and the Nakagami scale parameter is equal to the Gamma shape*scale. In my example, the Nakagami distribution would have a shape of 3, and a scale of 6. If this is true, mathematically, could anyone point me to a reference?