  We develop a general method to fit the planetary distribution function (PLDF)
to exoplanet survey data. This maximum likelihood method accommodates more than
one planet per star and any number of planet or target star properties.
Application to \Kepler data relies on estimates of the efficiency of
discovering transits around Solar type stars by Howard et al. (2011). These
estimates are shown to agree with theoretical predictions for an ideal transit
survey. Using announced \Kepler planet candidates, we fit the PLDF as a joint
powerlaw in planet radius, down to 0.5 R_Eart, and orbital period, up to 50
days. The estimated number of planets per star in this sample is ~ 0.7 --- 1.4,
where the broad range covers systematic uncertainties in the detection
efficiency. To analyze trends in the PLDF we consider four planet samples,
divided between shorter and longer periods at 7 days and between large and
small radii at 3 R_Earth. At longer periods, the size distribution of the small
planets, with index \alpha = -1.2 \pm 0.2 steepens to \alpha = -2.0 \pm 0.2 for
the larger planet sample. For shorter periods, the opposite is seen: smaller
planets follow a steep powerlaw, \alpha = -1.9 \pm 0.2 that is much shallower,
\alpha = -0.7 \pm 0.2 at large radii. The observed deficit of
intermediate-sized planets at the shortest periods may arise from the
evaporation and sublimation of Neptune and Saturn-like planets. If the trend
and explanation hold, it would be spectacular observational confirmation of the
core accretion and migration hypotheses, and allow refinement of these
theories.
