& Warren (1991), Warren et al. (1994) and Giallongo & Trevese (1990). The first one only takes into account the hydrogen clouds with column densities inferior or equal to $10^{17}~{\rm  cm}^{-2}$ (sometimes called the Ly$\alpha$ forest clouds). It will further be referred to as model A. The second one additionally includes systems with column densities between $10^{17}$ and $10^{20}~{\rm cm}^{-2}$ (sometimes called the Lyman limit systems). It will further be referred to as model B. As an extreme case, we also considered a model where a strong (10 magnitudes) absorption occurs in the Lyman continuum at a redshift very close to the one of the quasar, absorption which persists in the whole observable Lyman continuum. This model will further be referred to as model C. These three models are strongly inspired by those described by Royer (1994) where full details can be found. To fix ideas, it is worth noticing that the higher normalization of Madau (1995) puts his model between our models B and C.

It must be clear that the quasar spectrum defined above is only representative of an average quasar and that some individual quasar spectra deviate strongly from it. The true population of quasars will exhibit 