We use the H I-selected galaxy sample from the Arecibo Dual-Beam Survey of Rosenberg and Schneider to determine the shape of the H I mass function of galaxies in the local universe using both the stepwise maximum likelihood and the 1/tot methods. Our survey region spanned all 24 hours of right ascension at selected declinations between 8° and 29° covering ~430 deg2 of sky in the main beam. The survey is not as deep as some previous Arecibo surveys, but it has a larger total search volume and samples a much larger area of the sky. We conducted extensive tests on all aspects of the galaxy detection process, allowing us to empirically correct for our sensitivity limits, unlike the previous surveys. The mass function for the entire sample is quite steep, with a power-law slope of α ≈ -1.5. We find indications that the slope of the H I mass function is flatter near the Virgo Cluster, suggesting that evolutionary effects in high-density environments may alter the shape of the H I mass function. These evolutionary effects may help to explain differences in the H I mass function derived by different groups. We are sensitive to the most massive sources (log M 5 × 1010 M☉) over most of the declination range, ~1 sr, and do not detect any massive low surface brightness galaxies. These statistics restrict the population of Malin 1-like galaxies to less than 5.5 × 10-6 Mpc-3.
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