  (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.
