  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 and b =
3.03+/-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.
