  We study the Bose-Hubbard model in the presence of on-site disorder in the
canonical ensemble and conclude that the local density of the Bose glass phase
behaves differently at incommensurate filling than it does at commensurate one.
Scaling of the superfluid density at incommensurate filling of $\rho=1.1$ and
on-site interaction $U=80t$ predicts a superfluid-Bose glass transition at
disorder strength of $\Delta_c \approx 30t$. At this filling the local density
distribution shows skew behavior with increasing disorder strength.
Multifractal analysis also suggests a multifractal behavior resembling that of
the Anderson localization. Percolation analysis points to a phase transition of
percolating non-integer filled sites around the same value of disorder. Our
findings support the scenario of percolating superfluid clusters enhancing
Anderson localization near the superfluid-Bose glass transition. On the other
hand, the behavior of the commensurate filled system is rather different. Close
to the tip of the Mott lobe ($\rho=1, U=22t$) we find a Mott insulator-Bose
glass transition at disorder strength of $\Delta_c \approx 16t$. An analysis of
the local density distribution shows Gaussian like behavior for a wide range of
disorders above and below the transition.
