(Abridged) We investigate the EUV and X-ray flare rate distribution in radiated energy of the late-type active star AD Leo using long EUVE and BeppoSAX observations. We compare the observed light curves with light curves synthesized from model flares that are distributed in energy according to a power law with selectable index alpha (dN/dE ~ E^{-alpha}). Two methods are applied, the first comparing flux distributions of the binned data, and the second using the distributions of photon arrival time differences in the unbinned data. We find acceptable alpha values between 2.0-2.5 for the EUVE DS and the BeppoSAX LECS data. The BeppoSAX MECS data indicate a somewhat shallower energy distribution than the LECS data, which is attributed to the harder range of sensitivity of the MECS detector and the increasing peak temperatures of flares with increasing total (radiative) energy. The results suggest that flares can play an important role in the energy release of this active corona. We discuss caveats related to time variability, total energy, and multiple power-law distributions. Studying the limiting case of a corona that is entirely heated by a population of flares, we derive an expression for the time-averaged coronal differential emission measure distribution (DEM) that can be used as a diagnostic for the flare energy distribution. The shape of the analytical DEM agrees with previously published DEMs from observations of active stars.