Remarks on the phenomenological Tsallis distributions and their link with the Tsallis statistics

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 expressions for single-particle distribution functions (known as phenomenological distributions) particles obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics using factorization approximation. In spite of fact that this paper was published long time ago, its results are still extensively used in many fields physics, it is considered established connection between distributions statistics. Here we show result incorrect: mistake lies probability function definition generalized expectation values (of Tsallis-2 statistics), but calculated from standard normalized Tsallis-1) Considering which consistent with have proved (classical quantum) approximation differ distributions.