The stellar velocity distribution function ( DF ) in the solar vicinity is re-examined using data from the SDSS APOGEE survey ’ s DR16 and Gaia DR2 .
By exploiting APOGEE ’ s ability to chemically discriminate with great reliability the thin disk , thick disk and ( accreted ) halo populations , we can , for the first time , derive the three-dimensional velocity DFs for these chemically-separated populations .

We employ this smaller , but more data-rich APOGEE+ Gaia sample to build a data-driven model of the local stellar population velocity DFs , and use these as basis vectors for assessing the relative density proportions of these populations over 5 < R < 12 kpc , and -1.5 < z < 2.5 kpc range as derived from the larger , more complete ( i.e. , all-sky , magnitude-limited ) Gaia database .
We find that 81.9 \pm 3.1 \% of the objects in the selected Gaia data-set are thin-disk stars , 16.6 \pm 3.2 \% are thick-disk stars , and 1.5 \pm 0.1 \% belong to the Milky Way stellar halo .
We also find the local thick-to-thin-disk density normalization to be \rho _ { T } ( R _ { \odot } ) / \rho _ { t } ( R _ { \odot } ) = 2.1 \pm 0.2 \% , a result consistent with , but determined in a completely different way than , typical starcount/density analyses .
Using the same methodology , the local halo-to-disk density normalization is found to be \rho _ { H } ( R _ { \odot } ) / ( \rho _ { T } ( R _ { \odot } ) + \rho _ { t } ( R _ { \odot } ) ) = 1.2 \pm 0.6 \% , a value that may be inflated due to chemical overlap of halo and metal-weak thick disk stars .