We investigate the EUV and X-ray flare rate distribution in radiated energy of the late-type active star AD Leo .
Occurrence rates of solar flares have previously been found to be distributed in energy according to a power law , dN / dE \propto E ^ { - \alpha } , with a power-law index \alpha in the range 1.5 - 2.6 .
If \alpha \geq 2 , then an extrapolation of the flare distribution to low flare energies may be sufficient to heat the complete observable X-ray/EUV corona .

We have obtained long observations of AD Leo with the EUVE and BeppoSAX satellites .
Numerous flares have been detected , ranging over almost two orders of magnitude in their radiated energy .
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 .
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 ( for EUVE ) .
Subsets of the light curves are tested individually , and the quiescent flux has optionally been treated as a superposition of flares from the same flare distribution .
We find acceptable \alpha values between 2.0 - 2.5 for the EUVE DS and the BeppoSAX LECS data .
Some variation is found depending on whether or not a strong and long-lasting flare occurring in the EUVE data is included .
The BeppoSAX MECS data indicate a somewhat shallower energy distribution ( smaller \alpha ) than the simultaneously observed 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 .