Maximum-likelihood method for estimating the mass and period distributions of extrasolar planets

We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form dn = CM-alpha P-beta (dM/M)(dP/P), and find alpha = 0.11 +/- 0.10, beta = 0.27 +/- 0.06 for M less than or similar to 10 M-J, where M-J is the mass of Jupiter. The correlation coefficient between these two exponents is -0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range 1 M-J < M < 10 M-J, 2 d P < 10 yr.