Quantile estimation from grouped data: the cell midpoint

Abstract

Data are often collected in histogram form, especially in the context of computer simulation. While requiring less memory and computation than saving all observations, the grouping of observations in the histogram cells complicates statistical estimation of parameters of interest. In this paper the mean and variance of the cell midpoint estimator of the p^th quantile are analyzed in terms of distribution, cell width, and sample size. Three idiosyncrasies of using cell midpoints to estimate quantiles are illustrated. The results tend to run counter to previously published results for grouped data.

Keywords:

• simulation
• Monte Carlo
• histogram