  We have developed a parallel code called "VoIgt profile Parameter Estimation
Routine (VIPER)" for automatically fitting the H I Ly-$\alpha$ forest seen in
the spectra of QSOs. We obtained the H I column density distribution function
(CDDF) and line width ($b$) parameter distribution for $z < 0.45$ using spectra
of 82 QSOs obtained using Cosmic Origins Spectrograph and VIPER. Consistency of
these with the existing measurements in the literature validate our code. By
comparing this CDDF with those obtained from hydrodynamical simulation, we
constrain the H I photoionization rate ($\Gamma_{\rm HI}$) at $z < 0.45$ in
four redshift bins. The VIPER, together with the Code for Ionization and
Temperature Evolution (CITE) we have developed for GADGET-2, allows us to
explore parameter space and perform $\chi^2$ minimization to obtain
$\Gamma_{\rm HI}$. We notice that the $b$ parameters from the simulations are
smaller than what are derived from the observations. We show the observed $b$
parameter distribution and $b$ vs $\log {\rm N_{HI}}$ scatter can be reproduced
in simulation by introducing sub-grid scale turbulence. However, it has very
little influence on the derived $\Gamma_{\rm HI}$. The $\Gamma_{\rm HI}(z)$
obtained here, $(3.9 \pm 0.1) \times 10^{-14} \; (1+z)^{4.98 \pm 0.11} \;{\rm
s^{-1}}$, is in good agreement with those derived by us using flux based
statistics in the previous paper. These are consistent with the hydrogen
ionizing ultra-violet (UV) background being dominated mainly by QSOs without
needing any contribution from the non-standard sources of the UV photons.
