I am trying to compare power spectral density (PSD) estimates of two stochastic signals. I compute the attenuation by dividing one PSD by the other (both PSDs are computed and smoothed within the same frequency bins).
The PSD at a given frequency in each signal would be chi-squared distributed with 2 degrees of freedom.
If I take the ratio of two such chi-squared variates, I should get an F(2,2) distribution.
Now, I want to report this attenuation as a RMS value over frequency range. So I'm taking a mean square of a bunch of F(2,2) variates, and I don't know how to report the uncertainty of this RMS value. Can anyone help with suggestions on what to do or where to look?
Thank you for your help!