  The present study derives the distribution of secondary masses M2 for the 67
exoplanets and very low-mass brown dwarf companions of solar-type stars, known
as of April 4, 2001. This distribution is related to the distribution of M2 sin
i through an integral equation of Abel's type. Although a formal solution
exists for this equation, it is known to be ill-behaved, and thus very
sensitive to the statistical noise present in the input M2 sin i distribution.
To overcome that difficulty, we present two robust, independent approaches: (i)
the formal solution of the integral equation is numerically computed after
performing an optimal smoothing of the input distribution, (ii) the
Lucy-Richardson algorithm is used to invert the integral equation. Both
approaches give consistent results. The resulting statistical distribution of
exoplanet true masses reveals that there is no reason to ascribe the transition
between giant planets and brown dwarfs to the threshold mass for deuterium
ignition (about 13 MJ). The M2 distribution shows instead that all the objects
have M2 < 10 MJ, except the heavier candidates which cluster around 15 MJ.
