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Fig. 8

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Representation of the probability density of f given the observations  { dj }  (posterior distribution) as a function of the planetary systems frequency f, in the semimajor axis interval 5−320 AU and mass interval 3−14 MJup, for two detections around HR 8799 and β Pic (see Sect. 5.5 for details). The posterior distribution is obtained from Eq. (2) assuming a linear-flat prior for the frequency and a flat mass distribution for the planets. An equal-tail CI has been calculated using Eqs. (4) and (5) for confidence levels α of 68% (light grey area) and 95% (dark grey area). The dashed line gives the binomial distribution for two detections out of 42 targets, which represent the probability density that would be obtained in an ideal case where the observations would be sensitive to all planets in the range 5 − 320 AU and 3 − 14 MJup.

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