the variation of the fraction of obscured sources $f_{\mathrm{obs}}$ with luminosity measured by the recent medium (2–10keV) and hard (15–55keV) X-ray surveys of @Hasinger:2008ve and @Burlon:2011cr. In the 2–10keV band, from a combination of surveys performed by [*HEAO-1*]{}, [*ASCA*]{}, [*BeppoSAX*]{}, [*XMM-Newton*]{} and [*Chandra*]{} in the luminosity range $42\leq \log L_{\mathrm{X}} \leq 46$, @Hasinger:2008ve found $$\label{Eq:Hasinger}
f_{\mathrm{obs}}\simeq-0.226\log L_{\mathrm{X}}+10.342,$$ where $L_{\mathrm{X}}$ is the luminosity in the 2–10keV energy range. In the 15–55keV band, using [*Swift*]{}/BAT to study AGN in the luminosity range $42\leq \log L_{\mathrm{X}} \leq 45$, and fitting the data with $$\label{Eq:Burlon} 
f_{\mathrm{obs}}\simeq R_{\mathrm{low}}\,e^{-L_{\mathrm{HX}}/L_{\mathrm{C}}}+R_{\mathrm{high}}\,(1-e^{-L_{\mathrm{HX}}/L_{\mathrm{C}}}),$$ where $L_{\mathrm{HX}}$ is the luminosity in the 15–55keV band, @Burlon:2011cr obtained $R_{\mathrm{low}}=0.8$, $R_{\mathrm{high}}=0.2$ and $L_{\mathrm{C}}=10^{43.7}\rm\,erg\,s^{-1}$. We also used the results of the IR work of @Maiolino:2007bh, who found an anti-correlation between the ratio $\lambda L_{\lambda}(6.7\mu m)/\lambda L_{\lambda}(5100\AA)$ and the \[OIII\]$\lambda 5007\AA$ line luminosity. This trend was interpreted as an effect of the decrease of the covering factor of the circumnuclear dust as a function of luminosity, with $f_{\mathrm{obs}}$ varying as $$\label{Eq:Maiolino} 
 f_{\mathrm{obs}}\simeq \frac{1}{1+L_{\mathrm{opt}}^{0.414}},$$ where $L_{\mathrm{opt}}=(\lambda L_{\lambda}(5100\AA))/10^{45.63}$. Following @Maiolino:2007bh it is possible to rewrite $L_{\mathrm{opt}}$ as a function of the X-ray luminosity: $L_{\mathrm{opt}}=L_{\mathrm{X}}^{1.39}/10^{61.97}$.

The fraction of obscured sources at a given luminosity can be easily related to the 