We present a new accurate measurement of the H i mass function of galaxies from the HIPASS Bright Galaxy Catalog , a sample of 1000 galaxies with the highest H i peak flux densities in the southern ( \delta < 0 ^ { \circ } ) hemisphere ( Koribalski et al .
2003 ) .
This sample spans nearly four orders of magnitude in H i mass ( from \log ( \mbox { $M _ { HI } $ } / \mbox { $ { M } _ { \odot } $ } ) +2 \log h _ { 75 } = 6.8 to 10.6 ) and is the largest sample of H i selected galaxies to date .
We develop a bivariate maximum likelihood technique to measure the space density of galaxies , and show that this is a robust method , insensitive to the effects of large scale structure .
The resulting H i mass function can be fitted satisfactorily with a Schechter function with faint-end slope \alpha = -1.30 .
This slope is found to be dependent on morphological type , with later type galaxies giving steeper slopes .
We extensively test various effects that potentially bias the determination of the H i mass function , including peculiar motions of galaxies , large scale structure , selection bias , and inclination effects , and quantify these biases .
The large sample of galaxies enables an accurate measurement of the cosmological mass density of neutral gas : \Omega _ { HI } = ( 3.8 \pm 0.6 ) \times 10 ^ { -4 } h _ { 75 } ^ { -1 } .
Low surface brightness galaxies contribute only \sim 15 \% to this value , consistent with previous findings .