It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution .
Several properties of the Beta distribution make it a powerful tool for this purpose .
For example , the Beta distribution can reproduce a diverse range of probability density functions ( PDFs ) using just two shape parameters ( a and b ) .
We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis .
The Beta distribution is also uniquely defined over the interval zero to unity , meaning that it can serve as a proper prior for eccentricity when analysing the observations of bound extrasolar planets .
Using nested sampling , we find that the distribution of eccentricities for 396 exoplanets detected through radial velocity with high signal-to-noise is well-described by a Beta distribution with parameters a = 0.867 _ { -0.044 } ^ { +0.044 } and b = 3.03 _ { -0.16 } ^ { +0.17 } .
The Beta distribution is shown to be 3.7 times more likely to represent the underlying distribution of exoplanet eccentricities than the next best model : a Rayleigh + exponential distribution .
The same data are also used in an example population comparison utilizing the Beta distribution , where we find that the short- and long-period planets are described by distinct Beta distributions at a confidence of 11.6 \sigma and display a signature consistent with the effects of tidal circularization .