  We construct a maximum-likelihood algorithm - MAXLIMA, to derive the mass
distribution of the extrasolar planets when only the minimum masses are
observed. The algorithm derives the distribution by solving a numerically
stable set of equations, and does not need any iteration or smoothing. Based on
50 minimum masses, MAXLIMA yields a distribution which is approximately flat in
log M, and might rise slightly towards lower masses. The frequency drops off
very sharply when going to masses higher than 10 Jupiter masses, although we
suspect there is still a higher mass tail that extends up to probably 20
Jupiter masses. We estimate that 5% of the G stars in the solar neighborhood
have planets in the range of 1-10 Jupiter masses with periods shorter than 1500
days. For comparison we present the mass distribution of stellar companions in
the range of 100--1000 Jupiter masses, which is also approximately flat in log
M. The two populations are separated by the "brown-dwarf desert", a fact that
strongly supports the idea that these are two distinct populations. Accepting
this definite separation, we point out the conundrum concerning the
similarities between the period, eccentricity and even mass distribution of the
two populations.
