Confidence intervals for quantiles from histograms and other grouped data

Abstract

We introduce methods to obtain confidence intervals for quantiles when only grouped data are available. Our preferred method is to approximate the underlying density using the Generalized Lambda Distribution to estimate the quantiles and variance of the estimators. We compare this method with a frequency approximation approach and another method that uses a linear interpolation approximation of the density. Simulations show that intervals with excellent coverage can be found for a wide number of distributions, including those that are highly skewed distributions. We also apply our methods to real data sets highlighting how intervals can be computed from just histograms.