  We present a systematic study for the statistical fits of the transverse
momentum distributions of charged pions, Kaons and protons produced at energies
ranging between 7.7 and 2670 GeV to the extensive Boltzmann-Gibbs (BG) and the
nonextensive statistics (Tsallis as a special type and the generic axiomatic
nonextensive approach). We also present a comprehensive review on various
experimental parametrizations proposed to fit the transverse momentum
distributions of these produced particles. The inconsistency that the BG
approach is to be utilized in characterizing the chemical freezeout, while the
Tsallis approach in determining the kinetic freezeout is elaborated. The
resulting energy dependence of the different fit parameters largely varies with
the particle species and the degree of (non)extensivity. This manifests that
the Tsallis nonextensive approach seems to work well for p+p rather than for
A+A collisions. Drawing a complete picture of the utilization of Tsallis
statistics in modeling the transverse momentum distributions of several charged
particle produced at a wide range of energies and accordingly either disprove
or though confirm the relevant works are main advantages of this review. We
propose analytical expressions for the dependence of the fit parameters
obtained on the size of the colliding system, the energy, as well as the types
of the statistical approach applied. We conclude that the statistical
dependence of the various fit parameters, especially between Boltzmann and
Tsallis approaches could be understood that the statistical analysis ad hoc is
biased to the corresponding degree of extensivity (Boltzmann) or nonextensivity
(Tsallis). Alternatively, the empirical parameterizations, the other models,
and the generic (non)extensive approach seem to relax this biasness.
