  We introduce a new estimator of the peculiar velocity of a galaxy or group of
galaxies from redshift and distance estimates. This estimator results in
peculiar velocity estimates which are statistically unbiased and that have
errors that are Gaussian distributed, thus meeting the assumptions of analyses
that rely on individual peculiar velocities. We apply this estimator to the
SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact
that peculiar velocity estimates of distant galaxies are error dominated,
examine their error distributions, The adoption of the new estimator
significantly improves the accuracy and validity of studies of the large-scale
peculiar velocity field and eliminates potential systematic biases, thus
helping to bring peculiar velocity analysis into the era of precision
cosmology. In addition, our method of examining the distribution of velocity
errors should provide a useful check of the statistics of large peculiar
velocity catalogs, particularly those that are compiled out of data from
multiple sources.
