Moment estimation based on quantiles

We consider a moment estimation problem using empirical quantiles of the data. Specifically, we estimate the sample mean and the variance based only on the minimum, the quartiles, the median and the maximum values of the data. We propose a computational solution based on fitting a refined version of a generalized. distribution. Simulation results suggest that our method works reasonably well for a wide range of distributions. (C) 2013 Wiley Periodicals, Inc.