  [Abridged] We test the accuracy of different models of the attenuation of
light due to resonant scattering by intergalactic neutral hydrogen by comparing
their predictions of the evolution of the mean cosmic flux decrement, D_A, to
measurements of this quantity based on observations. To this end, we use data
available in the literature and our own measurements of the cosmic flux
decrement for 25 quasars in the redshift range 2.71 < z < 5.41 taken from the
SDSS Data Release 5. In order to perform the measurements of D_A, we fit a
power-law to the continuum redward of the Lya emission line, and extrapolate
this fit to region blueward of it, where the flux is severely affected by
absorption due to intervening HI absorbers. We compute, using numerical
simulations, the redshift evolution of D_A accounting for the presence of Lya
Forest absorbers and Lyman limit systems randomly distributed along the
line-of-sight, and compute its intrinsic scatter at the 1-, 2-, and 3-sigma
level due to fluctuations in the absorber properties (column density, Doppler
parameter, redshift) along different lines-of-sight. The numerical simulations
consist of Monte Carlo realizations of distributions of the absorber properties
constrained from observations. The results from the models considered here
confirm our theoretical expectation that the distribution of D_A at any given
redshift be well described by a lognormal distribution function. This implies
that the effective optical depth, usually defined as the negative logarithm of
the average flux, 1 - D_A, is very accurately Gaussian distributed, in contrast
to previous studies. This result is independent to the form of the input
distribution functions, and rather insensitive to the presence of high-column
density absorbers, such as the Lyman limit systems.
