  We use the INTEGRAL all-sky hard X-ray survey to perform a statistical study
of a representative sample of nearby AGN. Our entire all-sky sample consists of
127 AGN, of which 91 are confidently detected (>5 sigma) on the time-averaged
map obtained with the IBIS/ISGRI instrument and 36 are detected only during
single observations. Among the former there are 66 non-blazar AGN located at
|b|>5 deg, where the survey's identification completeness is ~93%, which we use
for calculating the AGN luminosity function and X-ray absorption distribution.
In broad agreement with previous studies, we find that the fraction of obscured
(log NH>22) objects is much higher (~70%) among the low-luminosity AGN
(Lx<10^43.6 erg/s) than among the high-luminosity ones (Lx>10^43.6 erg/s),
\~25%, where Lx is the luminosity in the 17-60 keV energy band. We also find
that locally the fraction of Compton-thick AGN is less than 20% unless there is
a significant population of AGN that are so strongly obscured that their
observed hard
  X-ray luminosities fall below 10^40-10^41 erg/s, the effective limit of our
survey. The constructed hard X-ray luminosity function has a canonical,
smoothly broken power-law shape in the range 40<log Lx<45.5 with a
characteristic luminosity of log L*=43.40+/-0.28. The estimated local
luminosity density due to AGN with log Lx>40 is (1.4+/-0.3) 10^39 erg/s/Mpc^3
(17-60 keV). We demonstrate that the spectral shape and amplitude of the CXB
are consistent with the simple scenario in which the NH distribution of AGN
(for a given
  Lx/L*(z) ratio has not changed significantly since z~1.5, while the AGN
luminosity function has experienced pure luminosity evolution.
