Quantum gas distributions prescribed by factorization hypothesis of probability

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 $q$.