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

Construction of Coupled Period-Mass Functions in Extrasolar Planets through the Nonparametric Approach