  Applying survival function analysis to the planet orbital period (P) and
semi-major axis (a) distribution from the Kepler sample, we find that all
exoplanets are uniformly distributed in (ln a) or (ln P), with an average inner
cut-off of 0.05 AU to the host star. More specifically, this inner cut-off is
0.04 AU for rocky worlds (1-2 Earth radii) and 0.08 AU for water worlds (2-4
Earth radii). Moreover, the transitional planets (4-10 Earth radii) and gas
giants (>10 Earth radii) have a change of slope of survival function at 0.4 AU
from -1 to -1/2, suggesting a different statistical distribution uniform in
\Sqrt[a] inside 0.4 AU, compared to small exoplanets (<4 Earth radii). This
difference in distribution is likely caused by the difference in planet
migration mechanism, and susceptibility to host stellar irradiation, for
gas-poor (<4 Earth radii) versus gas-rich (>4 Earth radii) planets. Armed with
this knowledge and combined with the survival function analysis of planet size
distribution, we can make precise estimates of planet occurrence rate and
predict the TESS mission yield.
