We investigate the estimation of orbital parameters by least-$chi^2$ Keplerian fits to radial velocity (RV) data using synthetic data sets. We find that while the fitted period is fairly accurate, the best-fit eccentricity and $M_psin i$ are systematically biased upward from the true values for low signal-to-noise ratio $K/sigmalesssim 3$ and moderate number of observations $N_{rm obs}lesssim 60$, leading to a suppression of the number of nearly circular orbits. Assuming intrinsic distributions of orbital parameters, we generate a large number of mock RV data sets and study the selection effect on the eccentricity distribution. We find the overall detection efficiency only mildly decreases with eccentricity. This is because although high eccentricity orbits are more difficult to sample, they also have larger RV amplitudes for fixed planet mass and orbital semi-major axis. Thus the primary source of uncertainties in the eccentricity distribution comes from biases in Keplerian fits to detections with low-amplitude and/or small $N_{rm obs}$, rather than from selection effects. Our results suggest that the abundance of low-eccentricity exoplanets may be underestimated in the current sample and we urge caution in interpreting the eccentricity distributions of low-amplitude detections in future RV samples.
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