How to discern the distribution function of mean-squared coherence values?
One approach might be an old method from "An approximation to the cumulative distribution function of the magnitude-squared coherence estimate" by Nutall and Carter (1981), who basically apply a non-linear distortion to transform the MSC to near-Gaussian random variables, then you could apply standard methods.

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1163657

A more recent approach used overlapping segments to create an (approximate) PDF and CDF for the MSC: "Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping" by Bortel and Sovka (2006):

http://www.sciencedirect.com/science/article/pii/S0165168406003471

They give a procedure for the comparison of two MSC estimates.

There may be more refined methods, but I'm not aware of them.