Amplitude distributions in time are related to correlations across frequency. In gaussian noise, the amplitudes and phases of the different frequency components are independent. In non-gaussian noise, even with white power spectrum, amplitudes and/or phases are correlated.
Do you have a reference for these statements? My understanding is that the amplitude distribution is largely irrelevant to the frequency content (for example if you take any signal and sort or permute it in time it sounds completely different yet retains the original amplitude distribution). Thanks, Paris