Bivariate Analysis of Distribution Functions Under Biased Sampling

Abstract

This article compares distribution functions among pairs of locations in their domains, in contrast to the typical approach of univariate comparison across individual locations. This bivariate approach is studied in the presence of sampling bias, which has been gaining attention in COVID-19 studies that over-represent more symptomatic people. In cases with either known or unknown sampling bias, we introduce Anderson–Darling-type tests based on both the univariate and bivariate formulation. A simulation study shows the superior performance of the bivariate approach over the univariate one. We illustrate the proposed methods using real data on the distribution of the number of symptoms suggestive of COVID-19.