Assuming that solar hard X-ray flares are caused by bremsstrahlung fro
m a distribution of accelerated electrons impinging on a thick target,
we determine the relationship between the total flare energy released
in the corona and observable flare parameters. It is shown that for t
he more numerous smaller flares to be energetically more important tha
n larger ones, there must be an anticorrelation between observed flux
and one or more of the photon spectral index, the total flare duration
, the ratio of the total energy that goes into heating the corona to t
he energy that goes into acceleration of electrons, and the reciprocal
of the low-energy cutoff of the accelerated electron spectrum. Using
a new statistical test which properly takes account of data truncation
due to observational selection effects, we find that neither spectral
index nor duration show an anticorrelation with flux in ISEE 3/ICE ha
rd X-ray data. Using a nonparametric method, we obtain single distribu
tions of peak flux, spectral index, duration, and fluence, corrected f
or selection biases. The functional forms of these distributions do no
t support coronal heating by numerous small flares without very specif
ic behavior by yet unobserved parameters.