In connection with Tsallis generalized statistical mechanics, we discu
ss the associated quantal distribution functions recently advanced by
Buyukkilic et al. [Phys. Lett. A 197 (1995) 209] and show, by recourse
to elementary considerations, that they can be regarded only as rathe
r rough approximations. Numerical calculations in a simple model show
that, for some values of the temperature and the chemical potential, r
esults obtained with the approximate distributions appreciably deviate
from the exact ones.