  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 distribution-free confidence intervals for such ratios are to
our knowledge not 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. 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.
