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We present a new accurate measurement of the HI mass function of galaxiesfrom the HIPASS Bright Galaxy Catalog, a sample of 1000 galaxies with thehighest HI peak flux densities in the southern hemisphere (Koribalski et al.2003). This sample spans nearly four orders of magnitude in HI mass (from logM_HI/M_sun=6.8 to 10.6, H0=75) and is the largest sample of HI selectedgalaxies to date. We develop a bivariate maximum likelihood technique tomeasure the space density of galaxies, and show that this is a robust method,insensitive to the effects of large scale structure. The resulting HI massfunction can be fitted satisfactorily with a Schechter function with faint-endslope alpha=-1.30. This slope is found to be dependent on morphological type,with later type galaxies giving steeper slopes. We extensively test variouseffects that potentially bias the determination of the HI mass function,including peculiar motions of galaxies, large scale structure, selection bias,and inclination effects, and quantify these biases. The large sample ofgalaxies enables an accurate measurement of the cosmological mass density ofneutral gas: Omega_HI=(3.8 +/- 0.6) x 10^{-4}. Low surface brightness galaxiescontribute only 15% to this value, consistent with previous findings.Comment: accepted for publication in Astronomical Journal, 16 pages, including  17 figures. Corrected typos and reference

The 1000 Brightest HIPASS Galaxies: The HiMass Function andHi

The 1000 Brightest HIPASS Galaxies: The HiMass Function and_Hi