Kepler exoplanets: a new method of population analysis
  This paper introduces a new method of inferring the intrinsic exoplanet population from Kepler data, based on the assumption that the frequency of exoplanets can be represented by a smooth function of planet radius and period. The method is applied to the two most recent data releases from the Kepler project, q1-16 and q1-17, over the range of periods 0.5 to 512 days, and radii 0.5 to 16 Earth radii. Both of these releases have known biases, with the first believed to contain excess false positives, and the second excess false negatives, so any analysis of them should be viewed with caution. We apply the new method of population estimation to these releases, treating them like practice data sets. With this method, we tentatively find that the average number of planets per star would be about $5.7\pm0.8$ for F stars, $5.0\pm0.2$ for G stars, $4.0\pm0.3$ for K stars, and $6.5\pm1.7$ for M stars, indicating a decreasing trend with FGK spectral type, but an upward jump for M stars. A second conclusion is that the number of planets per G star, per natural log unit of period (days) and radii (Earths) at the period and radius of the Earth around the Sun, is about $\Gamma_\oplus(G) = 1.1\pm 0.1$. A related parameter, $\eta_{\oplus}$, which in addition depends on the range of period and radius considered, is found to be $\eta_{\oplus}(G) \simeq 1.0 \pm 0.1 $. More definitive conclusions, and validation of these preliminary values, await the final release of Kepler's transiting exoplanet list. 
Wesley A. Traub
astro-ph.EP