  The Bose-Einstein and Fermi-Dirac statistics of the identified hadrons were
verified on the basis of the transverse momentum distributions of bosons and
fermions created in the $pp$ collisions at high energies using the
Tsallis-factorized statistics and the two-component distributions of the
Boltzmann-Gibbs statistics. The main differences between the parameters of the
Tsallis-factorized statistics and the Boltzmann-Gibbs statistics were
identified. The results of the Boltzmann-Gibbs statistics are reasonable and
suggest that the soft and hard hadrons may be produced from the two different
macroscopic states of the dynamical system. It was revealed that the volume of
the system obtained in the Tsallis-factorized statistics is unusually large in
comparison with the geometrical volume of two protons. The main formulas for
the Tsallis statistics in the grand canonical ensemble were formulated.
