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  d n = CM ^?α P ^?β(d M / M )(d P / P )  , and find  α= 0.11 ± 0.10  ,  β=?0.27 ± 0.06  for   M ? 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  .