The present work makes a contribution to the statistical analysis of medical time series. In particular, the work discusses the possibility of detecting the rate of fibrillation – observed in the atrium during atrial fibrillation - based solely on the statistical properties of ventricular interbeat-intervals. First the work concentrates on the statistical analysis of ECG-recordings and of ventricular tachograms. It presents a new method – the generation of so-called morphograms – which enables one to analyse the entire information carried by an ECG-recording without complicated pattern recognition. It is shown that this method is suitable for determining different states of health. Second the work concentrates on the analysis of the statistical properties of ventricular interbeat-intervals, observed during atrial fibrillation. It presents a new characteristic, statistical feature – an exponential decay in the distribution of those intervals - which has not been published before. Furthermore it is shown, that different statistical features of ventricular interbeat-intervals during atrial fibrillation are interrelated. In the following the work concentrates on the mathematical modelling of the physiological process during the conduction of atrial impulses through the AV node. In particular the work concentrates on the conduction model originally proposed by Jorgensen et al.. It is shown that this model can be fully analytical described. Based on a detailed discussion of the original model and mathematical solutions for modified ones, two methods for determining the fibrillation rate are presented. The performance of these methods are demonstrated based on medical data. The present work demonstrates that during atrial fibrillation the rate of fibrillation can be determined solely based on the statistical properties of ventricular interbeat-intervals.