It has been reported that the complexity characteristics of heart rate variability (HRV) in patients with permanent atrial fibrillation (AFib) based on multiscale entropy (MSE) analysis are associated with ischemic stroke risk. However, the interpretation of HRV complexity is not clear and the mathematical and physical relationships between HRV and ischemic stroke have not been established. MSE is determined not only by the correlation characteristics but also by probability density function characteristics. The aim of this study was to clarify which characteristics were important for the association between MSE and ischemic stroke risk in patients with permanent AFib. We analyzed 24 hours of HRV data from 173 patients with permanent AFib. Results show that long-range correlations like 1/f fluctuations in a range greater than 90s were observed in HRV time series in patients with AFib, but that these values had no predictive power as an ischemic stroke risk factor. On the other hand, probability density functions of coarse-grained scales greater than 2s were significantly associated with ischemic stroke risk. These results suggest that probability density functions are a useful risk factor for improving ischemic stroke risk assessment. To investigate the probability density function characteristics more in detail, we analyzed the asymmetric non-Gaussian properties of the probability distribution of HRV data. Part of this study was published in the journal Entropy .