  Using the period and mass data of two hundred and seventy-nine extrasolar
planets, we have constructed a coupled period-mass function through the
non-parametric approach. This analytic expression of the coupled period-mass
function has been obtained for the first time in this field. Moreover, due to a
moderate period-mass correlation, the shapes of mass/period functions vary as a
function of period/mass. These results of mass and period functions give way to
two important implications: (1) the deficit of massive close-in planets is
confirmed, and (2) the more massive planets have larger ranges of possible
semi-major axes. These interesting statistical results will provide important
clues into the theories of planetary formation.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics