  Using generic (non)extensive statistics, in which the underlying system
autonomously manifests its extensive and nonextensive statistical nature, we
extract various fit parameters from the CMS experiment and compare these to the
corresponding results obtained from Tsallis and Boltzmann statistics. The
present study is designed to indicate the possible variations between the three
types of statistical approaches and characterizes their dependence on collision
energy, multiplicity, and size of the system of interest. We analyze the
transverse momentum spectra $p_T$ of the strange hadrons \Kslxi produced in
Pb+Pb collisions, at 2.76 TeV, in p+Pb collisions, at 5.02 TeV, and in $p+p$
collisions, at 7 TeV. From the comparison of the resulting fit parameters;
temperature $T$, volume $V$, and nonextensvie parameter $d$, with calculations
based on Tsallis and Boltzmann statistics, remarkable differences between the
three types of statistics are determined besides a strong dependence on size
and type of the colliding system. We conclude that the produced particles with
large masses and large strange quantum numbers likely freeze out earlier than
the ones with smaller masses and less strange quantum numbers. This conclusion
seems not depending on the type of the particle or the collision but apparently
manifesting transitions from chemical (larger temperature) to the kinetic
freezeouts (lower temperature). For the first university (equivalent) class
c=1, the decrease in the second one, $d$, with increasing energy and collision
centrality highlights that the system departs from nonextensivity
(non-equilibrium) and apparently approaches extensivity (equilibrium)
indicating that the Boltzmann statistics becomes the proper statistical
approach in describing that system. Last but not least, we present analytical
expressions for the energy dependence of the various fit parameters.
