We have performed an extensive Voigt profile analysis of the neutral hydrogen (H i) and metal absorption present in a sample of 18 high-resolution, high signal-to-noise ratio quasi-stellar object (QSO) spectra observed with the Very Large Telescope Ultraviolet and Visual Echelle Spectrograph. We use this analysis to separate the metal contribution from the H i absorption and present an improved measurement of the flux probability distribution function (PDF) due to H i absorption alone at 〈z〉= 2.07, 2.52 and 2.94. The flux PDF is sensitive to the continuum fit in the normalized 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 H i absorption alone are systematically lower at 0.2 < F < 0.8 by up to 30 per cent compared to the widely used measurement of McDonald et al., based on a significantly smaller sample of Keck High Resolution Echelle Spectrometer 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 H i effective optical depth τeffH i at 1.7 < z < 4 is best fit with a single power law, , 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 ratio data.