  This paper uses numerical simulations to test the formation time distribution
of dark matter haloes predicted by the analytic excursion set approaches. The
formation time distribution is closely linked to the conditional mass function
and this test is therefore an indirect probe of this distribution. The
excursion set models tested are the extended Press-Schechter (EPS) model, the
ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB)
model. Three sets of simulations (6 realizations) have been used to investigate
the halo formation time distribution for halo masses ranging from dwarf-galaxy
like haloes ($M=10^{-3} M_*$, where $M_*$ is the characteristic non-linear mass
scale) to massive haloes of $M=8.7 M_*$. None of the models can match the
simulation results at both high and low redshift. In particular, dark matter
haloes formed generally earlier in our simulations than predicted by the EPS
model. This discrepancy might help explain why semi-analytic models of galaxy
formation, based on EPS merger trees, under-predict the number of high redshift
galaxies compared with recent observations.
