  (abridged) We study the hypothesis that observed X-ray/extreme ultraviolet
emission from coronae of magnetically active stars is entirely (or to a large
part) due to the superposition of flares, using an analytic approach to
determine the amplitude distribution of flares in light curves. The
flare-heating hypothesis is motivated by time series that show continuous
variability suggesting the presence of a large number of superimposed flares
with similar rise and decay time scales. We rigorously relate the amplitude
distribution of stellar flares to the observed histograms of binned counts and
photon waiting times, under the assumption that the flares occur at random and
have similar shapes. Applying these results to EUVE/DS observations of the
flaring star AD Leo, we find that the flare amplitude distribution can be
represented by a truncated power law with a power law index of 2.3 +/- 0.1. Our
analytical results agree with existing Monte Carlo results of Kashyap et al.
(2002) and Guedel et al. (2003). The method is applicable to a wide range of
further stochastically bursting astrophysical sources such as cataclysmic
variables, Gamma Ray Burst substructures, X-ray binaries, and spatially
resolved observations of solar flares.
