Visualizing Multiple Quantile Plots.
Multiple-quantile plots provide a powerful graphical method for comparing the distributions of two or more populations. This article develops a method of visualizing triple-quantile plots and their associated confidence tubes, thus extending the notion of a quantile-quantile (QQ) plot to three dimensions. More specifically, we consider three independent one-dimensional random samples with corresponding quantile functionsQ1,Q2, andQ3. The triple-quantile (QQQ) plot is then defined as the three-dimensional curveQ(p) = (Q1(p),Q2(p),Q3(p)), where 0 <p< 1. The empirical likelihood method is used to derive simultaneous distribution-free confidence tubes forQ. 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 in the online supplementary materials.
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
Marko A A
MA
Boon
Department of Econometrics & OR and CentER, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands.
John H J
JH
Einmahl
Department of Biostatistics, Columbia University, 722 West 168th Street, New York, NY 10032.
Ian W
IW
McKeague
Confidence region; Empirical likelihood; Three-sample comparison