Using a sample of 69,919 red giants from the SDSS-III/APOGEE Data Release 12, we measure the distribution of stars in the [$\alpha$/Fe] vs. [Fe/H] plane and the metallicity distribution functions (MDF) across an unprecedented volume of the Milky Way disk, with radius $311$ kpc. The peak of the midplane MDF shifts to lower metallicity at larger $R$, reflecting the Galactic metallicity gradient. Most strikingly, the shape of the midplane MDF changes systematically with radius, with a negatively skewed distribution at $31$ kpc or [$\alpha$/Fe]$>0.18$, the MDF shows little dependence on $R$. The positive skewness of the outer disk MDF may be a signature of radial migration; we show that blurring of stellar populations by orbital eccentricities is not enough to explain the reversal of MDF shape but a simple model of radial migration can do so.
Comment: Submitted, 18 pages, 16 figures