We present total infrared (IR) and ultraviolet (UV) luminosity functions derived from large representative samples of galaxies at z ~ 0, selected at IR and UV wavelengths from the IRAS IIFSCz catalogue, and the GALEX AIS respectively. We augment these with deep Spitzer and GALEX imaging of galaxies in the 11 Mpc Local Volume Legacy Survey (LVL), allowing us to extend these luminosity functions to lower luminosities (~10^6 L_sun), and providing good constraints on the slope of the luminosity function at the extreme faint end for the first time. Using conventional star formation prescriptions, we generate from our data the SFR distribution function for the local Universe. We find that it has a Schechter form, that the faint-end slope has a constant value (to the limits of our data) of {alpha} = -1.51 pm 0.08, and the characteristic SFR is 9.2 M_sun/yr. We also show the distribution function of the SFR volume density; we then use this to calculate a value for the total SFR volume density at z ~ 0 of 0.025 pm 0.0016 M_sun/yr/Mpc^-3, of which ~ 20% is occurring in starbursts. Decomposing the total star formation by infrared luminosity, it can be seen that 9 pm 1% is due to LIRGs, and 0.7 pm 0.2% is occuring in ULIRGs. By comparing UV and IR emission for galaxies in our sample, we also calculate the fraction of star formation occurring in dust obscured environments, and examine the distribution of dusty star formation: we find a very shallow slope at the highly extincted end, which may be attributable to line of sight orientation effects as well as conventional internal extinction.
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