  We fit a log-normal function to the M dwarf orbital surface density
distribution of gas giant planets, over the mass range 1-10 times that of
Jupiter, from 0.07-400 AU. We use a Markov Chain Monte Carlo approach to
explore the likelihoods of various parameter values consistent with point
estimates of the data given our assumed functional form. This fit is consistent
with radial velocity, microlensing, and direct imaging observations, is
well-motivated from theoretical and phenomenological viewpoints, and makes
predictions of future surveys. We present probability distributions for each
parameter as well as a Maximum Likelihood Estimate solution. We suggest this
function makes more physical sense than other widely used functions, and
explore the implications of our results on the design of future exoplanet
surveys.
