  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.
