We have developed a parallel code called the VoIgt profile Parameter Estimation Routine (VIPER) for automatically fitting the HI Ly{alpha} forest seen in the spectra of quasi-stellar objects (QSOs). We obtained the HI column density distribution function (CDDF) and linewidth (b) parameter distribution for z<0.45 using spectra of 82 QSOs obtained using the Cosmic Origins Spectrograph and VIPER. The consistency of these with existing measurements in the literature validates our code. By comparing this CDDF with those obtained from hydrodynamical simulations, we constrain the H I photoionization rate ({Gamma}_HI_) at z<0.45 in four redshift bins. VIPER, together with the Code for Ionization and Temperature Evolution (CITE), which we developed for GADGET-2, allows us to explore parameter space and perform {chi}^2^ minimization to obtain {Gamma}_HI_. We notice that the b parameters from the simulations are smaller than those derived from observations. We show that the observed b parameter distribution and b versus logNHI scatter can be reproduced in simulations by introducing subgrid-scale turbulence. However, it has very little influence on the derived {Gamma}_HI_. The {Gamma}_HI_(z) obtained here, (3.9+/-0.1)x10^-14^(1+z)^4.98+/-0.11^s^-1^, is in good agreement with the values derived by us using flux-based statistics in a previous article. These values are consistent with the hydrogen ionizing ultraviolet (UV) background being dominated mainly by QSOs, without needing any contribution from non-standard sources of UV photons.