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A determination of the initial mass function (IMF) of the current, incompletecensus of the 10 Myr-old TW Hya association (TWA) is presented. This census isbuilt from a literature compilation supplemented with new spectra and 17 newradial velocities, as well as a re-analysis of Hipparcos data that confirmed HR4334 (A2Vn) as a member. Though the dominant uncertainty in the IMF remainscensus incompleteness, a detailed statistical treatment is carried out to makethe IMF determination independent of binning, while accounting for small numberstatistics. The currently known high-likelihood members are fitted by alog-normal distribution with a central mass of $0.21^{+0.11}_{-0.06}$$M_{\odot}$ and a characteristic width of $0.8^{+0.2}_{-0.1}$ dex in the 12$M_{\rm Jup}$-2 $M_{\odot}$ range, whereas a Salpeter power law with $\alpha =2.2^{+1.1}_{-0.5}$ best describes the IMF slope in the $0.1-2$ $M_{\odot}$range. This characteristic width is higher than other young associations, whichmay be due to incompleteness in the current census of low-mass TWA stars. Atentative overpopulation of isolated planetary-mass members similar to 2MASSJ11472421-2040204 and 2MASS J11193254-1137466 is identified: this indicatesthat there might be as many as $10^{+13}_{-5}$ similar members of TWA withhot-start model-dependent masses estimated at $\sim$ 5-7 $M_{\rm Jup}$, most ofwhich would be too faint to be detected in 2MASS. Our new radial velocitymeasurements corroborate the membership of 2MASS J11472421-2040204, and secureTWA 28 (M8.5$\gamma$), TWA 29 (M9.5$\gamma$) and TWA 33 (M4.5e) as members. Thediscovery of 2MASS J09553336-0208403, a young L7-type interloper unrelated toTWA, is also presented.

BANYAN. IX. The Initial Mass Function and Planetary-Mass Object Space Density of the TW Hya Association