  We have performed an extensive Voigt profile analysis of the neutral hydrogen
(HI) and metal absorption present in a sample of 18 high resolution, high
signal-to-noise QSO spectra observed with VLT/UVES. We use this analysis to
separate the metal contribution from the HI absorption and present an improved
measurement of the flux probability distribution function (PDF) due to HI
absorption alone at <z> = 2.07, 2.52, and 2.94. The flux PDF is sensitive to
the continuum fit in the normalised flux range 0.8 < F < 1.0 and to metal
absorption at 0.2 < F < 0.8. Our new measurements of the flux PDF due to HI
absorption alone are systematically lower at 0.2 < F < 0.8 by up to 30%
compared to the widely used measurement of McDonald et al. (2000), based on a
significantly smaller sample of Keck/HIRES data. This discrepancy is probably
due to a combination of our improved removal of the metal absorption and cosmic
variance, since variations in the flux PDF between different lines-of-sight are
large. The HI effective optical depth at 1.7 < z < 4 is best fit with a single
power law, (0.0023 +-0.0007) (1+z)^(3.65 +- 0.21), in good agreement with
previous measurements from comparable data. As also found previously, the
effect of noise on the flux distribution is not significant in high resolution,
high signal-to-noise data.
