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We have measured the X-ray spectral properties of a complete flux-limitedsample of bright AGNs from HEAO-1 all-sky catalogs to investigate theirstatistics and provide greater constraints on the bright-end of the hard X-rayluminosity function (HXLF) of AGNs and the AGN population synthesis model ofthe X-ray background. Spectral studies using data from ASCA, XMM-Newton and/orBeppo-SAX observations have been made for almost all AGNs in this sample.  The spectral measurements enable us to construct the neutral absorbing columndensity (Log nH) distribution and separate HXLFs for absorbed (Log nH[cm-2]>21.5) and unabsorbed AGNs in the local universe. Our results show evidence fora difference in the shapes of HXLFs of absorbed and unabsorbed AGNs in thatabsorbed AGN HXLF drops more rapidly at higher luminosities than that ofunabsorbed AGNs, which is similar to that previously reported. In the Lx - nHplot, we found no AGN in the high-luminosity high-intrinsic absorption regime(Log Lx[erg/s]> 44.5, Log nH[cm-2]> 21.5) in our sample, where we expect about5 AGNs if we assume that absorbed and unabsorbed having identical AGN HXLFshapes. We also find that the observed flux with ASCA or XMM-Newton is smallerthan that with HEAO-1 by a factor of 0.29 on average, which is expected forre-observation of sources with a factor 2.5 variability amplitude scale.Comment: 43 pages(one column), 10 figures(5 electronic only figures have been  included in the preprint source (tar.gz file)), accepted by The Astronomical  Journal, 9. Mar 200

Spectral Statistics and Local Luminosity Function of a Complete Hard X-Ray Sample of the Brightest Active Galactic Nuclei