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Visualizing Multiple Quantile Plots.

ABSTRACT: 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 functions Q1, Q2, and Q3. 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 in the online supplementary materials.

SUBMITTER: Boon MA 

PROVIDER: S-EPMC3899392 | biostudies-literature | 2013 Mar

REPOSITORIES: biostudies-literature

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Visualizing Multiple Quantile Plots.

Boon Marko A A MA   Einmahl John H J JH   McKeague Ian W IW  

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20130301 1

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 functions <i>Q</i><sub>1</sub>, <i>Q</i><sub>2</sub>, and <i>Q</i><sub>3</sub>. The t  ...[more]

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