  We propose a new method for investigating the exclusion statistics of
quasi-particles in Conformal Field Theory (CFT) spectra. The method leads to
one-particle distribution functions, which generalize the Fermi-Dirac
distribution. For the simplest $su(n)$ invariant CFTs we find a generalization
of Gentile parafermions, and we obtain new distributions for the simplest
$Z_N$-invariant CFTs. In special examples, our approach reproduces
distributions based on `fractional exclusion statistics' in the sense of
Haldane. We comment on applications to fractional quantum Hall effect edge
theories.
