The statistical properties of ventricular (RR) interbeat intervals during atrial fibrillation exhibit several characteristic features, such as a linear relation between the local mean and standard deviation obtained in small time windows (constant signal to noise ratio), a crossover in the power spectrum from a 1/f type at low frequencies to a white noise behaviour at high frequencies, and an exponential tail in the distribution of long RR intervals. We show in this work that these characteristic features are interrelated. The linear relation between the local mean and standard deviation can be used to classify the RR interval into two groups, where one gives the dominant contribution to the 1/f part of the power spectrum and the other the dominant contribution to the white noise part. Remarkably, the long RR intervals only contribute to the latter. Our results are useful to improve the characterisation of AF based on non-invasive surface ECG recordings.