Extreme Point Methods in the Study of Classes of Bivariate Distributions and some Applications to Contingency Tables

摘要

The set of all bivariate positive distributions is neither compact nor convex. But the set of all bivariate positive quadrant distributions with fixed marginals is a convex set. These convex sets are compact in the case of discrete bivariate distributions if the marginals have finite support. A simple method to enumerate the extreme points of these convex sets is given. In the context of contingency tables for testing the null hypothesis independence against the alternative positive quadrant dependence one can use the method of extreme point analysis to compare the performance of various tests. Keywords: Extreme point; Convex set; Compact set; Bivariate distributions; Positive quadrant dependence; Negative quadrant dependence; and Power function and contingency tables.