AGN luminosity function over a wide luminosity range.

Broad-line QSOs were identified using the PRIMUS spectra and excluded from the @Aird12 samples. In these sources the AGN emission dominates over the host galaxy at optical wavelengths, precluding measurements of the stellar mass of the host galaxy. Over the X-ray luminosities probed by @Aird12, ${L_\mathrm{X}}=10^{42-44}$ [$\mathrm{erg\;s^{-1}}$]{}, the broad-line QSOs correspond to $\lesssim 20$% of the AGN population. However, the broad-line fraction increases with luminosity [e.g. @Steffen03; @Treister09b] and thus excluding broad-line QSOs may bias the slope of the $\lambda$ distribution measured by @Aird12. On the other hand, previous studies have found that QSOs may be predominantly high accretion rate sources, accreting close to their Eddington limit (e.g. @Kollmeier06 [@Trump11], but see also @Kelly13) and dominate the population at ${L_\mathrm{X}}>10^{44}$ [$\mathrm{erg\;s^{-1}}$]{}. Our models (described below) that extrapolate the $\lambda$ distribution to higher accretion rates may therefore account for the bulk of the broad-line QSO population. We discuss remaining issues regarding the exclusion of broad-line QSOs in Section \[sec:discuss\].

The X-ray luminosity function of AGNs {#sec:xlf}
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The AGN luminosity function traces the overall distribution of accretion activity in AGNs in terms of the observed luminosities at a particular waveband. Any model that 