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 _ { \oplus } , and orbital period , up to 50 days .
The estimated number of planets per star in this sample is \sim 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 _ { \oplus } .
At longer periods , the size distribution of the small planets , with index \alpha \simeq - 1.2 \pm 0.2 steepens to \alpha \simeq - 2.0 \pm 0.2 for the larger planet sample .
For shorter periods , the opposite is seen : smaller planets follow a steep powerlaw , \alpha \simeq - 1.9 \pm 0.2 that is much shallower , \alpha \simeq - 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 .