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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!

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