#### von Hippel, P. T.,Scarpino, S. V.,Holas, I.

Researchers often estimate income inequality by using data that give only the number of cases (e.g., families or households) whose incomes fall in "bins" such as $0 to$9,999, $10,000 to$14,999,..., >= \$200,000. We find that popular methods for estimating inequality from binned incomes are not robust in small samples, where popular methods can produce infinite, undefined, or arbitrarily large estimates. To solve these and other problems, we develop two improved estimators: a robust Pareto midpoint estimator (RPME) and a multimodel generalized beta estimator (MGBE). In a broad evaluation using U.S. national, state, and county data from 1970 to 2009, we find that both estimators produce very good estimates of the mean and Gini coefficient but less accurate estimates of the Theil index and mean log deviation. Neither estimator is uniformly more accurate, but the RPME is much faster, which may be a consideration when many estimates must be obtained from many data sets. We have made the methods available as the rpme and mgbe commands for Stata and the binequality package for R.