Exoplanet masses derived from RVs

We present a new method for estimating the probability density distribution (density) of the unprojected quantity from such samples. For a sample of n data values, the method involves solving n simultaneous linear equations to determine the weights of delta functions for the raw, unsmoothed density of the unprojected quantity that cause the associated cumulative distribution function (CDF) of the projected quantity to exactly reproduce the empirical CDF of the sample at the locations of the n data values.

We smooth the raw density using nonparametric kernel density estimation with a normal kernel of bandwidth {sigma}. We calibrate the dependence of {sigma} on n by Monte Carlo experiments performed on samples drawn from a theoretical density, in which the integrated square error is minimized. We scale this calibration to the ranges of real RV samples using the Normal Reference Rule.