Multiscale cumulative residual distribution entropy and its applications on heart rate time series

Distribution entropy has been proved to reveal stability for short time series and to distinguish different classes of series by complexity. However, there still exists some drawbacks. For example, it does not consider the possible causality underlying the data, which may not precisely identify deterministic from stochastic processes. In addition, cumulative residual entropy can successfully solve such problems and identify randomness and complexity of time series quite clearly. We therefore combine distribution entropy with cumulative residual entropy named cumulative residual distribution entropy (CRDE), aiming at considering both distribution and values of distances in the state space. CRDE can detect the temporal and spatial structures of the series after adding multiscale analysis. Results show that the combined method can characterize series from stochastic system (white noise and 1/f noise) and deterministic system (chaotic and periodic series). Then, we apply it to physiological signals, and the result is consistent with the one that loss of complexity at larger scales is related to aging and disease.