  Most astrophysical plasmas are observed to have velocity distribution
functions exhibiting non-Maxwellian suprathermal tails. The high energy
particle populations are accurately represented by the family of
kappa-distributions where the use of these distributions has been unjustly
criticized because of a perceived lack of theoretical justification. We show
that distributions very close to kappa-distributions are a consequence of the
generalized entropy favored by nonextensive statistics, which provides the
missing link for power-law models of non-thermal features from fundamental
physics. With regard to the the physical basis supplied by the Tsallis
nonextensive entropy formalism we propose that this slightly modified
functional form, qualitatively similar to the traditional kappa-distribution,
be used in fitting particle spectra in the future.
