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We construct a maximum-likelihood algorithm - MAXLIMA, to derive the massdistribution of the extrasolar planets when only the minimum masses areobserved. The algorithm derives the distribution by solving a numericallystable set of equations, and does not need any iteration or smoothing. Based on50 minimum masses, MAXLIMA yields a distribution which is approximately flat inlog M, and might rise slightly towards lower masses. The frequency drops offvery sharply when going to masses higher than 10 Jupiter masses, although wesuspect there is still a higher mass tail that extends up to probably 20Jupiter masses. We estimate that 5% of the G stars in the solar neighborhoodhave planets in the range of 1-10 Jupiter masses with periods shorter than 1500days. For comparison we present the mass distribution of stellar companions inthe range of 100--1000 Jupiter masses, which is also approximately flat in logM. The two populations are separated by the "brown-dwarf desert", a fact thatstrongly supports the idea that these are two distinct populations. Acceptingthis definite separation, we point out the conundrum concerning thesimilarities between the period, eccentricity and even mass distribution of thetwo populations.Comment: 19 pages, 3 figures, submitted to The Astrophysical Journa

Derivation of the Mass Distribution of Extrasolar Planets with MAXLIMA, a Maximum Likelihood Algorithm