Although nonlinear dynamics are known to determine the behaviour of individual neurons, an emerging consensus is that large-scale neocortical activity can be characterised as a Gaussian process. This view arises from both modelling and behavioural studies of the brain. Hence nonlinearity at this scale is seen to herald pathological states such as seizures. We analysed the temporal fluctuations in human electrocencephalographic (EEG) recordings acquired from healthy human subjects and estimated the likely probability distribution function(s) across a range of temporal scales. At many time scales (e.g. 20 Hz) such fluctuations deviate significantly from fitted Gaussian distributions, with a bias towards a power-law scaling at the high amplitude end, reflecting extremal events in the EEG which would not be expected to occur in a Gaussian field. Fits to the data can be better captured by the exponential family of noise distributions. Within the traditional alpha range (~10 Hz), activity typically shows a distinct bimodal distribution. Hence, whilst Gaussian models capture much of the signal variation in macroscopic brain signals, they are unable to explain these distinct phenomena. Are such deviations from a Gaussian model important and what alternative models, such as fractional kinetics, should be explored?