  We report the predictions of different Monte Carlo event generators including
HIJING, Pythia, and QGSJETII in comparison with the experimental data measured
by the CMS Collaboration at CERN in proton-proton ($pp$) collisions at
center-of-mass energy $\sqrt{s}$ = 0.9 and 2.36 TeV. The CMS experimental
transverse momentum ($p_T$ or $p_{\perp}$) spectra of charged hadrons were
measured for pseudorapidity range 0 $\le$ $\eta$ $\le$ 2.4 with bin width of
$\eta$ = 0.2 (for $p_T$ from 0.1 to 2 GeV/$c$) and a single bin of $\eta$ for
$\lvert$$\eta$$\rvert$ $<$ 2.4 (for $p_T$ from 0.1 to 4 GeV/$c$). Pythia
reproduced the $p_T$ spectra with reasonable agreement for most of the $p_T$
range. It depicts better results in the case of the $|\eta|<$ 2.4 than HIJING
and QGSJETII which could reproduce the spectra in a limited $p_T$ range.
Furthermore, to analyze the $p_T$ spectra of charged hadrons measured by the
CMS Collaboration, we used a three component function (structured from the
Boltzmann distribution) and the $q$-dual function (from the $q$-dual
statistics) to extract parameter values relevant for the study of bulk
properties of hadronic matter at high energy. We have also applied the two
analytic functions over the model predictions. The values extracted by the
functions from the HIJING and Pythia models are closer to the experimental data
than the QGSJETII model. Although the models could reproduce the $p_T$ spectra
of all charged particles in some of the $p_T$ range but none of them could
reproduce the distributions over the entire $p_T$ range and in all the
pseudorapidity regions.
