Visualizing Multiple Quantile Plots

Multiple quantile plots provide a powerful graphical method for comparing the distributions of two or more populations. This paper develops a method of visualizing triple quantile plots and their associated confidence tubes, thus extending the notion of a QQ plot to three dimensions. More specifically, we consider three independent one-dimensional random samples with corresponding quantile functions Q1, Q2 and Q3, respectively. The triple quantile (QQQ) plot is then defined as the three-dimensional curve Q(p) = (Q1(p);Q2(p);Q3(p)); where 0 <p <1. The empirical likelihood method is used to derive simultaneous distribution-free confidence tubes for Q. We apply our method to an economic case study of strike durations, and to an epidemiological study involving the comparison of cholesterol levels among three populations. These data as well as the Mathematica code for computation of the tubes are available online.