Log-normal surface density distribution of 1–10 M_J companions to M dwarfs. On the left axis we plot the integrated values of f, where the black points correspond to the data points listed in Table 1: note the horizontal lines are ranges, while the vertical lines are errors in f. On theright axis, we show the relative values of the differential PDFs. In red, we show the MLE fit as described in the text. The integrated f values for the MLE, over the ranges in semimajor axis corresponding to the data from Table 1, are shown as a red cross. We show in blue the fit from Clanton & Gaudi (2016) that was published before the results of Lannier et al. (2016) were available.