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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 (δ < 0°) hemisphere. This sample spans nearly 4 orders of magnitude in H I mass log (MH I/ M⊙) + 2 log h75 = 6.8-10.6 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 α = -1.30. This slope is found to be dependent on morphological type, with late-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 we quantify these biases. The large sample of galaxies enables an accurate measurement of the cosmological mass density of neutral gas: ΩH I = (3.8 ± 0.6) × 10-4 h75-1. Low surface brightness galaxies contribute only ∼ 15% to this value, consistent with previous findings.
Zwaan et al. (Sun,) studied this question.