  The distributions of solar flare energies and waiting times have not been
described simultaneously by a single physical model, yet. In this research, we
investigate whether recent avalanche models can describe the distributions for
both the released energies and waiting times of flares in an active region.
Flaring events are simulated using the modified Lu and Hamilton model (Lu and
Hamilton (1991), ApJ, 380, 89) and also the optimized model (Farhang et al.
(2018), ApJ, 859, 41). Applying a probability balance equation approach, we
study the statistics of the simulated flaring events and investigate the origin
of the observed power law in the flare frequency-size distribution. The results
indicate that the power law originates in the distribution of transition rates
(the distribution of the probabilities of transitions between different
energies) rather than the distribution of the energy of the active region. It
is also observed that the waiting-time distribution of simulated flaring events
follows a q-exponential function which approximates a simple Poisson
distribution.
