Comparator: Noisy sine to square wave, how much phase noise?
Depending on how the spectral density is provided, it is essentially asin 

Determine the phase error due to the hysteresis: 

\$ \Theta_{low} = sin^{-1}(-0.3) \$

\$ \Theta_{high} = sin^{-1}(0.3) \$

This is the phase error purely due to the hysteresis if a pure sinewave was applied. 

Assuming you have or have converted your spectral density into magnitude &amp; equally assuming it is normally distributed. generate the MEAN and 1 standard deviation.

LOW:

\$ \Theta_{low_error\_mean} = sin^{-1}(-0.3) - sin^{-1}(-0.3 + mean) \$

\$ \Theta_{low\_error\_+\sigma} = sin^{-1}(-0.3) -sin^{-1}(-0.3 + \sigma) \$

HIGH:

\$ \Theta_{high\_error\_mean} = sin^{-1}(0.3) - sin^{-1}(0.3 + mean) \$

\$ \Theta_{high\_error\_+\sigma} = sin^{-1}(0.3) -sin^{-1}(0.3 + \sigma) \$

With the mean and the standard deviation "phase error" you can reconstruct a phase error distribution curve.

However... if the spectral density isn't normally distributed you will need to derive errors at a number of specific points to reconstruct a phase error curve specific to the information you have