Distribution of ﹩{\hat{S}}_{21}^{3/2}{\rm{d}}N/{\rm{d}}\mathrm{log}{\hat{S}}_{21}﹩ vs. ﹩\mathrm{log}{\hat{S}}_{21}﹩ from the HI galaxies with S/N ≥ 6.5, in the ALFALFA (blue) and FATHOMER (red), to evaluate the completeness. In the FATHOMER, we can join the Code 1 and Code 2 candidates. The vertical dashed lines represent the flux where the survey completeness is 90%. The 90% completeness is according to the fit of ﹩{\hat{S}}_{21,90 \% }﹩, and the corresponding logarithmic values are 0.10 for FATHOMER and 0.034 for ALFALFA.