  It is well accepted that unabsorbed as well as absorbed AGN are needed to
explain the nature and the shape of the Cosmic X-ray background, even if the
fraction of highly absorbed objects (dubbed Compton-thick sources)
substantially still escapes detection. We derive and analyze the absorption
distribution using a complete sample of AGN detected by Swift-BAT in the first
three years of the survey. The fraction of Compton-thick AGN represents only
4.6% of the total AGN population detected by Swift-BAT. However, we show that
once corrected for the bias against the detection of very absorbed sources the
real intrinsic fraction of Compton-thick AGN is 20$^{+9}_{-6}$%. We proved for
the first time (also in the BAT band) that the anti-correlation of the fraction
of absorbed AGN and luminosity it tightly connected to the different behavior
of the luminosity functions (XLFs) of absorbed and unabsorbed AGN. This points
towards a difference between the two subsamples of objects with absorbed AGN
being, on average, intrinsically less luminous than unobscured ones. Moreover
the XLFs show that the fraction of obscured AGN might also decrease at very low
luminosity. This can be successfully interpreted in the framework of a disk
cloud outflow scenario as the disappearance of the obscuring region below a
critical luminosity. Our results are discussed in the framework of population
synthesis models and the origin of the Cosmic X-ray Background.
