We pay particular attention to the high end of the Lyα optical depth distribution of a quasar spectrum. Based on the flux distribution (Miralda-Escudé et al.), a simple yet seemingly cosmological model-differentiating statistic, Δ—the cumulative probability of a quasar spectrum with Lyα optical depth greater than a high-value τ₀—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 Δ_τ0: 0.13 for the former versus 0.058 for the latter, for τ₀ = 3.0 at z = 3. Moreover, it is argued that Δ_τ0 may be fairly robust to compute theoretically because it does not seem to depend sensitively on small variations of simulation parameters such as the radiation field, cooling, the feedback process, radiative transfer, the resolution, and the simulation volume within the plausible ranges of the concerned quantities. Furthermore, it is illustrated that Δ_τ0 can be obtained sufficiently accurately from currently available observed quasar spectra for τ₀ ~ 3.0-4.0, when observational noise is properly taken into account. We anticipate that analyses of observations of quasar Lyα 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 Ω₀, Ω_0,HDM, and Λ₀.