Comparison of 1000 draws from the unobscured and obscured AGN E(B − V) distributions used in this work. The distributions are based on the XXL AGN E(B − V) distribution derived in Fotopoulou et al. (2016b, grey shaded). The XXL-QSO distribution (blue) is the distribution found for XXL AGN assigned the QSO class template and is used for unobscured AGN in this work. The XXL-AGN distribution (red) is constructed for all XXL sources not assigned the QSO class and is used for obscured AGN in this work. For comparison, we also include the E(B − V) distribution found for SDSS quasars (green, Hopkins et al. 2004).