The impact of distance uncertainties on local luminosity and mass functions

In order to investigate discrepancies between recent published estimates of the the HI mass function (HIMF), we explore the impact of distance uncertainties on the derivation of the faint end slope of mass and luminosity functions of galaxies in the local volume by deriving HIMFs from mock HI surveys. We consider various survey geometries and depths and compare the HIMFs measured when using ``real'' distances, distances derived by assuming pure Hubble flow and distances assigned from parametric models of the local velocity field. The effect is variable and dependent on the exact survey geometry, but can easily lead to incorrect estimates of the HIMF, particularly at the low mass end. We show that at least part of the discrepancies among recent derivations of the HIMF can be accounted for by the use of different methods to assign distances. We conclude that a better understanding of the local velocity field will be necessary for accurate determinations of the local galaxy luminosity and mass functions.