We use the H I-selected galaxy sample from the Arecibo Dual-Beam Survey ( Rosenberg & Schneider 2000 ) to determine the shape of the H I mass function of galaxies in the local universe using both the step-wise maximum likelihood and the 1 / { \cal V } _ { tot } methods .
Our survey region spanned all 24 hours of right ascension at selected declinations between 8 ^ { \circ } and 29 ^ { \circ } covering \sim 430 deg ^ { 2 } 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 \alpha \approx - 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 \times 10 ^ { 10 } M _ { \mathord { \odot } } ) over most of the declination range , \sim 1 sr , and do not detect any massive low surface brightness galaxies .
These statistics restrict the population of Malin 1-like galaxies to < 5.5 \times 10 ^ { -6 } Mpc ^ { -3 } .