  We use an automated Voigt-profile fitting procedure to extract statistical
properties of the Ly$\alpha$ forest in a numerical simulation of an $\Omega=1$,
cold dark matter (CDM) universe. Our analysis method is similar to that used in
most observational studies of the forest, and we compare the simulations to
recently published results derived from Keck HIRES spectra. With the
Voigt-profile decomposition analysis, the simulation reproduces the large
number of weak lines ($N_{\rm HI}\la 10^{14} cm^{-2}$) found in the HIRES
spectra. At $z=3$, the $b$-parameter distribution has a median of $35\kms$ and
a dispersion of $20\kms$, in reasonable agreement with the observed values. The
comparison between our new analysis and recent data strengthens earlier claims
that the Ly$alpha$ forest arises naturally in hierarchical structure formation
as photoionized gas falls into dark matter potential wells.
