We compare subhalo mass and velocity functions obtained from different simulations with different subhalo finders among each other , and with predictions from the new semi-analytical model of Jiang & van den Bosch ( 2014 ) .
We find that subhalo mass functions ( SHMFs ) obtained using different subhalo finders agree with each other at the level of \sim 20 percent , but only at the low mass end .
At the massive end , subhalo finders that identify subhaloes based purely on density in configuration space dramatically underpredict the subhalo abundances by more than an order of magnitude .
These problems are much less severe for subhalo velocity functions ( SHVFs ) , indicating that they arise from issues related to assigning masses to the subhaloes , rather than from detecting them .
Overall the predictions from the semi-analytical model are in excellent agreement with simulation results obtained using the more advanced subhalo finders that use information in six dimensional phase-space .
In particular , the model accurately reproduces the slope and host-mass-dependent normalization of both the subhalo mass and velocity functions .
We find that the SHMFs and SHVFs have power-law slopes of 0.82 and 2.6 , respectively , significantly shallower than what has been claimed in several studies in the literature .