  From the Tsallis unnormalized (or Tsallis-2) statistical mechanical
formulation, B\"{u}y\"{u}kkili\c{c} {\it et al.} [Phys. Lett. A 197, 209
(1995)] derived the expressions for the single-particle distribution functions
(known as the phenomenological Tsallis distributions) for particles obeying the
Maxwell-Boltzmann, Bose-Einstein and the Fermi-Dirac statistics using the
factorization approximation. In spite of the fact that this paper was published
long time ago, its results are still extensively used in many fields of
physics, and it is considered that it was this paper that established the
connection between the phenomenological Tsallis distributions and the Tsallis
statistics. Here we show that this result is incorrect: the mistake lies in the
fact that the probability distribution function was derived using the
definition of the generalized expectation values (of the Tsallis-2 statistics),
but the single-particle distribution function was calculated from this
probability distribution using the standard definition of the expectation
values of the Tsallis normalized (or Tsallis-1) statistics. Considering the
definition of the expectation values which is consistent with the Tsallis-2
formulation, we have proved that the single-particle (classical and quantum)
distribution functions in the factorization approximation differ from the
phenomenological Tsallis distributions.
