SIMBAD references

We examine the eccentricity distribution(s) of radial velocity (RV) detected exoplanets. Previously, the eccentricity distribution was found to be described well by a Beta distribution with shape parameters $a=0.867\,\mathrm{ and}\, b=3.03$. Increasing the sample size by a factor of 2.25, we find that the cumulative distribution function regression method now prefers a mixture model of Rayleigh + Exponential distributions over the Beta distribution, with an increase in Bayesian evidence of $\Delta \ln {Z}\sim 77$ ($12.6\, \sigma$). Using probability density function regression, the eccentricity distribution is best described by a Gamma distribution, with a Rayleigh + Exponential mixture a close second. The mixture model parameters, $\alpha = 0.68\pm 0.05, \lambda =3.32\pm 0.25,\,\mathrm{ and}\, \sigma =0.11\pm 0.01$, are consistent between methods. We corroborate findings that exoplanet eccentricities are drawn from independent parent distributions when splitting the sample by period, mass, and multiplicity. Systems with a known outer massive companion provide no positive evidence for an eccentricity distribution distinct from those without. We quantitatively show M-dwarf hosted planets share a common eccentricity distribution with those orbiting FGK-type stars. We release our PYTHON code, ECCENTRICIPY, which allows bespoke tailoring of the input archive to create more relevant priors for particular problems in RV planet discovery and characterization. We re-characterized example planets using either traditional Beta, or updated priors, finding differences for recovery of low-amplitude multisignal systems. We explore the effects of a variety of prior choices. The accurate determination of small but non-zero eccentricity values has wide-ranging implications for modelling the structure and evolution of planets and their atmospheres due to the energy dissipated by tidal flexing.