A Statistical Analysis of X-Ray Bursts Using Mutual Information

A statistical study on solar flares stronger than C1 class detected by the Geostationary Operational Environmental Satellite from 1975 to 2017 was performed. A sequence of waiting times (time elapsed between adjacent X-ray flare peaks) was constructed from the data. A surrogate waiting time distribution is produced using a non-stationary Poisson distribution defined by a time dependent firing rate derived from the data using a sliding window. Utilizing Shannon entropy, the mutual information of the original and surrogate waiting time sequences is then computed at various look-aheads. It is shown that the observed waiting time sequence has a mutual information greater than the constructed sequence that is statistically significant at relatively small timescales. This suggests there is structure not sufficiently captured by a non-stationary Poisson distribution, despite representing the observed distribution well (Moon et al., 2001).