The irregular fluctuations of solar flare emissions, as determined from terrestrial neutron monitors, remains poorly understood. These records empirically revealed a temporally-related variance to mean power law, $1/f$ noise and a non-Gaussian distribution, all features indicative of self-organized criticality, a theory of how derministic dynamical systems can spontaneously evolve to unstable states that express erratic changes. The non-Gaussian distribution found here approximated a Tweedie compound Poisson exponential dispersion model, a statistical distribution characterized by a variance to mean power law that itself can imply $1/f$ noise. Tweedie exponential dispersion models serve a primary role in statistical theory as foci for weak convergence for a wide range of random distributions, a role which supports an alternative conjecture to explain the solar flare fluctuations as being based on random processes rather than a deterministic system.
"The snap, crackle and pop of solar flares explained." Braz. J. Probab. Stat. 35 (1) 101 - 118, February 2021. https://doi.org/10.1214/20-BJPS497