  The supermassive black hole at the centre of the Galaxy flares at least daily
in the infrared (IR) and X-ray bands, yet the process driving these flares is
still unknown. So far detailed analysis has only been performed on a few bright
flares. In particular, the broadband spectral modelling suffers from a strong
lack of simultaneous data. However, new monitoring campaigns now provide data
on thousands of flaring events, allowing a statistical analysis of the flare
properties. In this paper, we investigate the X-ray and IR flux distributions
of the flare events. Using a self-consistent calculation of the particle
distribution, we model the statistical properties of the flares. Based on a
previous work on single flares, we consider two families of models: pure
synchrotron models and synchrotron self-Compton (SSC) models. We investigate
the effect of fluctuations in some relevant parameters (e.g. acceleration
properties, density, magnetic field) on the flux distributions. The
distribution of these parameters is readily derived from the flux distributions
observed at different wavelengths. In both scenarios, we find that fluctuations
of the power injected in accelerated particles plays a major role. This must be
distributed as a power-law (with different indices in each model). In the
synchrotron dominated scenario, we derive the most extreme values of the
acceleration power required to reproduce the brightest flares. In that model,
the distribution of the acceleration slope fluctuations is constrained and in
the SSC scenario we constrain the distributions of the correlated magnetic
field and flow density variations.
