  We calculate the condensate fraction and the condensate and non-condensate
spatial and momentum distribution of the Bose-Hubbard model in a trap. From our
results, it is evident that using approximate distributions can lead to
erroneous experimental estimates of the condensate. Strong interactions cause
the condensate to develop pedestal-like structures around the central peak that
can be mistaken as non-condensate atoms. Near the transition temperature, the
peak itself can include a significant non-condensate component. Using
distributions generated from QMC simulations, experiments can map their
measurements for higher accuracy in identifying phase transitions and
temperature.
