Cumulative incidence rate of LAHs, dn/dz(LAH,  M₁₅₀₀ ≤ M_1500, 0), as a function of M_1500, 0. The blue solid line and shading show the dn/dz(LAH,  M₁₅₀₀ ≤ M_1500, 0) at z ≃ 3.65 and the uncertainty, respectively. The uncertainty is propagated from the 1σ error of the X_LAH for all the sources. The solid black and green lines indicate M₁₅₀₀ of the brightest source in our sample and the upper limit of M₁₅₀₀ for the UV-bright sample, respectively (the M₁₅₀₀ of the faintest source is −18 mag). The blue dashed thin and thick lines represent the dn/dz for DLAs and DLAs+sub-DLAs at z = 3.65 calculated from the best-fit formulae of the z evolution of absorbers in Zafar et al. (2013a).