We propose a new method for investigating the exclusion statistics of
quasiparticles in conformal field theory (CFT) spectra. The method lea
ds to one-particle distribution functions, which generalize the Fermi-
Dirac distribution. For the simplest SU(n) invariant CFTs we find a ge
neralization of Gentile parafermions, and we obtain new distributions
for the simplest Z(N)-invariant CFTs. In special examples, our approac
h reproduces distributions based on ''fractional exclusion statistics'
' in the sense of Haldane. We comment on applications to fractional qu
antum Hall effect edge theories.