Ratios of sample percentiles or of quantiles based on a single sample are often
published for skewed income data to illustrate aspects of income inequality, but distributionfree
confidence intervals for such ratios are not available in the literature. Here we derive
and compare two large-sample methods for obtaining such intervals. They both require
good distribution-free estimates of the quantile density at the quantiles of interest, and such
estimates have recently become available. Simulation studies for various sample sizes are
carried out for Pareto, lognormal and exponential distributions, as well as fitted generalized
lambda distributions, to determine the coverage probabilities and widths of the intervals.
Robustness of the estimators to contamination or a positive proportion of zero incomes is
examined via influence functions and simulations. The motivating example is Australian
household income data where ratios of quantiles measure inequality, but of course these
results apply equally to data from other countries.

EB00000002098K

Available

• When large n is not enough – Distribution-free interval estimators for ratios of quantiles