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We have made a Monte Carlo simulation of the intergalactic absorption in order to model the Lyman continuum absorption, which is required to estimate the escape fraction of the Lyman continuum from distant galaxies. To input into the simulation, we derive an empirical distribution function of the intergalactic absorbers which reproduces recent observational statistics of the Lyman α forest, Lyman limit systems (LLSs) and damped Lyman α systems (DLAs) simultaneously. In particular, we assume a common functional form of the number evolution along the redshift for all types of absorbers. The Lyman series transmissions in our simulation reproduce the observed redshift evolution of the transmissions excellently, and the Lyman continuum transmission also agrees with an observed estimation which is still quite rare in the literature. The probability distribution of the Lyman α opacity in our simulation is lognormal with a tail towards a large opacity. This tail is produced by DLAs. The probability distribution of the Lyman continuum opacity in our simulation also shows a broad tail towards a large opacity. This tail is produced by LLSs. Because of the rarity of LLSs, we have a chance to have a clean line of sight in the Lyman continuum even for   z ∼ 4  with a probability of about 20 per cent. Our simulation expects a good correlation between the Lyman continuum opacity and the Lyman α opacity, which may be useful to estimate the former from the latter for an individual line of sight.

A Monte Carlo simulation of the intergalactic absorption and the detectability of the Lyman continuum from distant galaxies