Two-dimensional bivariate HI mass–L_r distribution of the NIBLES sample, derived using only HI detections. Main panel a: log(Φ(M)ΔM) as a function of both HI mass (in M_⊙) and L_r (in L_⊙). Upper panel b: the summation of the main panel over HI mass, which reproduces the input M09 luminosity function, while right panel c: HIMF, the summation of the bivariate distribution over luminosity. Since the highest HI mass bin in this distribution (log(M_HI) = 10.75) is not fully sampled, we plotted its position in the HIMF (panel c) at the mean value of the measured HI masses contained within the bin rather than at its normal M_HI midpoint. We did not plot the point for the lowest HI mass bin (log(M_HI) = 6.25) in the HIMF (panel c) since it was populated with partial occupation numbers only, due to the relatively high fractional HI mass uncertainty of these sources.