  Nonextensive quantum gas distributions are investigated on the basis of the
factorization hypothesis of compound probability required by thermodynamic
equilibrium. It is shown that the formalisms of Tsallis nonextensive
statistical mechanics with normalized average give distribution functions for
standard bosons and fermions obeying Pauli principle. The formalism with
unnormalized average leads to a intermediate quantum distribution comparable to
that of fractional exclusion statistics, with Fermi surface at T=0 depending on
the parameter $q$.
