Quantum gas distribution prescribed by factorization hypothesis of probability

Nonextensive quantum gas distributions are revisited on the basis of the factorization hypothesis of compound probability required by the thermal equilibrium in nonextensive systems. 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 an intermediate quantum distribution comparable to that of fractional exclusion statistics, with Fermi surface at T=0 depending on the parameter q.