  We pay particular attention to the high end of the $\lya$ optical depth
distribution of a quasar spectrum. Based on the flux distribution
(Miralda-Escud\'e et al 1996), a simple yet seemingly cosmological model
-differentiating statistic, $\Delta_{\tau_0}$ -- the cumulative probability of
a quasar spectrum with $\lya$ optical depth greater than a high value $\tau_0$
-- is emphasized. It is shown that two different models -- the cold dark matter
model with a cosmological constant and the mixed hot and cold dark matter
model, both normalized to COBE and local galaxy cluster abundance -- yield
quite different values of $\Delta_{\tau_0}$: 0.13 of the former versus 0.058 of
the latter for $\tau_0=3.0$ at $z=3$. Moreover, it is argued that
$\Delta_{\tau_0}$ may be fairly robust to compute theoretically because it does
not seem to depend sensitively on small variations of simulations parameters
such as radiation field, cooling, feedback process, radiative transfer,
resolution and simulation volume within the plausible ranges of the concerned
quantities. Furthermore, it is illustrated that $\Delta_{\tau_0}$ can be
obtained sufficiently accurately from currently available observed quasar
spectra for $\tau_0\sim 3.0-4.0$, when observational noise is properly taken
into account. We anticipate that analyses of observations of quasar $\lya$
absorption spectra over a range of redshift may be able to constrain the
redshift evolution of the amplitude of the density fluctuations on
small-to-intermediate scales, therefore providing an independent constraint on
$\Omega_0$, $\Omega_{0,HDM}$ and $\Lambda_0$.
