We calculate an empirical, non-parametric estimate of the shape of the period-marginalized radius distribution of planets with periods less than 150?days using the small yet well-characterized sample of cool (T eff 4000 K) dwarf stars in the Kepler catalog. In particular, we present and validate a new procedure, based on weighted kernel density estimation, to reconstruct the shape of the planet radius function down to radii smaller than the completeness limit of the survey at the longest periods. Under the assumption that the period distribution of planets does not change dramatically with planet radius, we show that the occurrence of planets around these stars continues to increase to below 1 R ⊕, and that there is no strong evidence for a turnover in the planet radius function. In fact, we demonstrate using many iterations of simulated data that a spurious turnover may be inferred from data even when the true distribution continues to rise toward smaller radii. Finally, the sharp rise in the radius distribution below ~3 R ⊕ implies that a large number of planets await discovery around cool dwarfs as the sensitivities of ground-based transit surveys increase.
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机译：我们使用开普勒中的冷（T eff <4000 K）矮人恒星的小而特征充分的样本，计算了小于150天的周期的边际半径分布的形状的经验，非参数估计目录。特别是，我们提出并验证了一种基于加权核密度估计的新程序，该程序可以在最长的时间段内将半径减小到半径小于勘测完整性极限的行星半径函数。假设行星的周期分布不会随行星半径的变化而显着变化，我们表明这些恒星周围的行星的出现继续增加到1 R below以下，并且没有强有力的证据证明行星半径发生转换功能。实际上，我们证明了使用模拟数据的多次迭代，即使真实分布继续朝着较小的半径上升，也可能会从数据中推断出虚假周转。最后，在〜3 R below以下半径分布的急剧上升意味着随着地面过境调查的敏感性增加，大量的行星正等待在冷矮人周围发现。
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