We derive kinematic distances to the 86 6.7 GHz methanol masers discovered in the Arecibo Methanol Maser Galactic Plane Survey .
The systemic velocities of the sources were derived from ^ { 13 } CO ( J = 2 - 1 ) , CS ( J = 5 - 4 ) , and NH _ { 3 } observations made with the ARO Submillimeter Telescope , the APEX telescope , and the Effelsberg 100 m telescope , respectively .
Kinematic distance ambiguities were resolved using H I self-absorption with H I data from the VLA Galactic Plane Survey .
We observe roughly three times as many sources at the far distance compared to the near distance .
The vertical distribution of the sources has a scale height of \sim 30 pc , and is much lower than that of the Galactic thin disk .
We use the distances derived in this work to determine the luminosity function of 6.7 GHz maser emission .
The luminosity function has a peak at approximately 10 ^ { -6 } ~ { } L _ { \sun } .
Assuming that this luminosity function applies , the methanol maser population in the Large Magellanic Cloud and M33 is at least 4 and 14 times smaller , respectively , than in our Galaxy .