The velocity width function (WF) of galaxies. Red squares correspond to the WF of galaxies measured in the Local Volume by Klypin et al. (2015). The Local Volume WF is based on a nearly volume-complete optical catalog of nearby galaxies (Karachentsev et al. 2013), and includes both late-type and early-type dwarfs. Blue circles correspond to the WF measured in this work, based on the galaxy catalog of the ALFALFA HI survey (Haynes et al. 2011). The W< 40km s^-1 section of the ALFALFA WF (blue dots) is not used in the analysis that follows, due to possible incompleteness issues (see Sect. 2.1.1 for details). In both cases, the errorbars represent the uncertainties due to counting statistics only.