  Based on Sloan Digital Sky Survey (SDSS) photometric data, Gu developed a new
Monte-Carlo-based method for estimating the stellar metallicity distribution
functions (MDFs). This method enables a more reliable determination of MDFs
compared with the conventional polynomial-based methods. In this work, MDF
determined from the method are well fit by three-Gaussian model, with peaks at
${\rm [Fe/H]}$=$-0.68$, $-1.38$, and $-1.90$, associated with the thick disk,
inner halo, and outer halo, respectively. The vertical metallicity gradient
within $1<Z<5\,{\rm kpc}$ is ${\rm d}\langle{\rm [Fe/H]}\rangle/{\rm d}Z\approx
-0.19\,{\rm dex}\cdot{\rm kpc}^{-1}$ around $R=8.25\,{\rm kpc}$. But the mean
radial gradient is almost negligible. The density profile of the thick disk is
fitted with modified double exponential law decaying to a constant at far
distance. The scale height and scale length thus estimated are $H\approx
1.13\,{\rm kpc}$ and $L\approx 3.63\,{\rm kpc}$, which are in consistent with
the results determined from star-counts method in previous studies. The halos
are described with two-axial power-law ellipsoid and the axis ratios of both
inner halo and outer halo, inferred from stellar number density in $R$-$Z$
plane, are $q_{ih}\approx 0.49$ and $q_{oh}\approx 0.61$, respectively. It also
manifests that the outer halo is a more spherical than inner halo. Moreover,
the halo power-law indices estimated are $n_{ih}\approx 3.4$ and $n_{oh}\approx
3.1$, indicating that the stellar number density of inner halo changes more
steeper than that of outer halo.
